G. Biondini and E. Fagerstrom, “The integrable nature of modulational instability,” SIAM J. Appl. Math. 75, 136–163 (2015).

[Crossref]

W. Chen, Z. Song, and Z. Meng, “Periodical spectral holes along fiber dispersion at the second-order modulation instability sideband,” Opt. Quantum Electron. 47, 3427–3434 (2015).

[Crossref]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photonics 8, 755–764 (2014).

[Crossref]

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4, 011054 (2014).

V. E. Zakharov and A. A. Gelash, “Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability,” Nonlinearity 27, R1–R39 (2014).

[Crossref]

V. E. Zakharov and A. A. Gelash, “Nonlinear stage of modulation instability,” Phys. Rev. Lett. 111, 054101 (2013).

[Crossref]
[PubMed]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).

[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375, 2029 (2011).

[Crossref]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–115 (2011).

[Crossref]
[PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

A. Bendahmane, A. Mussot, P. Szriftgiser, O. Zerkak, G. Genty, J. M. Dudley, and A. Kudlinski, “Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber,” Opt. Lett. 39, 4490–4493 (2011).

[Crossref]

S. Wabnitz and N. Akhmediev, “Efficient modulation frequency doubling by induced modulation instability,” Opt. Commun. 283, 1152–1154 (2010).

[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Exp. 17, 21497–21508 (2009).

[Crossref]

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238, 540–548 (2009).

[Crossref]

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 18, 11185 (2007).

[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[Crossref]

P. Kylemark, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Semi-analytic saturation theory of fiber optical parametric amplifiers,” J. Lightwave Technol. 24, 3471–3479 (2006).

[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B. 3, 477–486 (2002).

[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[Crossref]
[PubMed]

A. Osborne, “The random and deterministic dynamics of rogue waves in unidirectional, deep-water wave trains,” Marine structures 14, 275–293 (2001).

[Crossref]

M. E. Marhic, K. K. Y. Wong, M. C. Ho, and L. G. Kazovsky, “92% Pump depletion in a continuous-wave one-pump fiber optical parametric amplifier,” Opt. Lett. 26, 620–622 (2001).

[Crossref]

M. J. Ablowitz, J. Hammack, D. Henderson, and C.M. Schober, “Modulated periodic Stokes waves in deep water,” Phys. Rev. Lett. 84, 887–890 (2000).

[Crossref]
[PubMed]

A. Calini and C. M. Schober, “Homoclinic chaos increases the likelihood of rogue wave formation,” Phys. Lett. A. 298, 335–349 (2000).

[Crossref]

E. Seve, G. Millot, and S. Trillo, “Strong four-photon conversion regime of cross-phase modulation induced modulational instability,” Phys. Rev. E. 61, 3139–3150 (2000).

[Crossref]

G. Millot, E. Seve, S. Wabnitz, and S. Trillo, “Observation of a novel large-signal four-photon instability in optical wave mixing,” Phys. Rev. Lett. 80, 504–507 (1998).

[Crossref]

S. Trillo, G. Millot, E. Seve, and S. Wabnitz, “Failure of phase matching concept in large-signal parametric frequency conversion,” Appl. Phys. Lett. 72, 150–152 (1997).

[Crossref]

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B. 8, 824–840 (1991).

[Crossref]

G. Cappellini and S. Trillo, “Energy conversion in degenerate four-photon mixing in birefringent fibers,” Opt. Lett. 16, 895–897 (1991).

[Crossref]
[PubMed]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16, 986–988 (1991).

[Crossref]
[PubMed]

S. Trillo and S. Wabnitz, “Self-injected spatial mode locking and coherent all-optical FM/AM switching based on modulational instability,” Opt. Lett. 16, 1566–1568 (1991)

[Crossref]
[PubMed]

M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM J. Appl. Math. 50, 339–351 (1990).

[Crossref]

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 69, 1089–1093 (1987).

[Crossref]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[Crossref]
[PubMed]

N. N. Akhmediev, V.M. Eleonoskii, and N.E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894 (1985).

H. C. Yuen and W. E. Ferguson, “Relationship between Benjamin-Feir instability and recurrence in the nonlinear Schrödinger equation,” Phys. Fluids 21, 1275 (1978).

[Crossref]

T. B. Benjamin and J. E. Feir, “The disintegration of wavetrains on deep water. Part 1: Theory,” J. Fluid Mech. 27, 417–430 (1967).

[Crossref]

V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307 (1966).

A. Vedenov and L. I. Rudakov, “Interaction of waves in continuous media,” Sov. Phys. Dokl. 9, 1073 (1965).

M. J. Ablowitz, J. Hammack, D. Henderson, and C.M. Schober, “Modulated periodic Stokes waves in deep water,” Phys. Rev. Lett. 84, 887–890 (2000).

[Crossref]
[PubMed]

M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM J. Appl. Math. 50, 339–351 (1990).

[Crossref]

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4, 011054 (2014).

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

S. Wabnitz and N. Akhmediev, “Efficient modulation frequency doubling by induced modulation instability,” Opt. Commun. 283, 1152–1154 (2010).

[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Exp. 17, 21497–21508 (2009).

[Crossref]

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 69, 1089–1093 (1987).

[Crossref]

N. N. Akhmediev, V.M. Eleonoskii, and N.E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894 (1985).

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).

[Crossref]

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 18, 11185 (2007).

[Crossref]

T. B. Benjamin and J. E. Feir, “The disintegration of wavetrains on deep water. Part 1: Theory,” J. Fluid Mech. 27, 417–430 (1967).

[Crossref]

V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307 (1966).

G. Biondini and E. Fagerstrom, “The integrable nature of modulational instability,” SIAM J. Appl. Math. 75, 136–163 (2015).

[Crossref]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).

[Crossref]

A. Calini and C. M. Schober, “Homoclinic chaos increases the likelihood of rogue wave formation,” Phys. Lett. A. 298, 335–349 (2000).

[Crossref]

W. Chen, Z. Song, and Z. Meng, “Periodical spectral holes along fiber dispersion at the second-order modulation instability sideband,” Opt. Quantum Electron. 47, 3427–3434 (2015).

[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[Crossref]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photonics 8, 755–764 (2014).

[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Exp. 17, 21497–21508 (2009).

[Crossref]

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4, 011054 (2014).

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photonics 8, 755–764 (2014).

[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375, 2029 (2011).

[Crossref]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–115 (2011).

[Crossref]
[PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

A. Bendahmane, A. Mussot, P. Szriftgiser, O. Zerkak, G. Genty, J. M. Dudley, and A. Kudlinski, “Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber,” Opt. Lett. 39, 4490–4493 (2011).

[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Exp. 17, 21497–21508 (2009).

[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[Crossref]

N. N. Akhmediev, V.M. Eleonoskii, and N.E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894 (1985).

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B. 3, 477–486 (2002).

[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[Crossref]
[PubMed]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photonics 8, 755–764 (2014).

[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375, 2029 (2011).

[Crossref]

G. Biondini and E. Fagerstrom, “The integrable nature of modulational instability,” SIAM J. Appl. Math. 75, 136–163 (2015).

[Crossref]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–115 (2011).

[Crossref]
[PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

T. B. Benjamin and J. E. Feir, “The disintegration of wavetrains on deep water. Part 1: Theory,” J. Fluid Mech. 27, 417–430 (1967).

[Crossref]

H. C. Yuen and W. E. Ferguson, “Relationship between Benjamin-Feir instability and recurrence in the nonlinear Schrödinger equation,” Phys. Fluids 21, 1275 (1978).

[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–115 (2011).

[Crossref]
[PubMed]

V. E. Zakharov and A. A. Gelash, “Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability,” Nonlinearity 27, R1–R39 (2014).

[Crossref]

V. E. Zakharov and A. A. Gelash, “Nonlinear stage of modulation instability,” Phys. Rev. Lett. 111, 054101 (2013).

[Crossref]
[PubMed]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photonics 8, 755–764 (2014).

[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

A. Bendahmane, A. Mussot, P. Szriftgiser, O. Zerkak, G. Genty, J. M. Dudley, and A. Kudlinski, “Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber,” Opt. Lett. 39, 4490–4493 (2011).

[Crossref]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375, 2029 (2011).

[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Exp. 17, 21497–21508 (2009).

[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[Crossref]

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 18, 11185 (2007).

[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B. 3, 477–486 (2002).

[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[Crossref]
[PubMed]

M. J. Ablowitz, J. Hammack, D. Henderson, and C.M. Schober, “Modulated periodic Stokes waves in deep water,” Phys. Rev. Lett. 84, 887–890 (2000).

[Crossref]
[PubMed]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–115 (2011).

[Crossref]
[PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[Crossref]
[PubMed]

M. J. Ablowitz, J. Hammack, D. Henderson, and C.M. Schober, “Modulated periodic Stokes waves in deep water,” Phys. Rev. Lett. 84, 887–890 (2000).

[Crossref]
[PubMed]

M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM J. Appl. Math. 50, 339–351 (1990).

[Crossref]

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 18, 11185 (2007).

[Crossref]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–115 (2011).

[Crossref]
[PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Exp. 17, 21497–21508 (2009).

[Crossref]

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 69, 1089–1093 (1987).

[Crossref]

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4, 011054 (2014).

A. Bendahmane, A. Mussot, P. Szriftgiser, O. Zerkak, G. Genty, J. M. Dudley, and A. Kudlinski, “Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber,” Opt. Lett. 39, 4490–4493 (2011).

[Crossref]

N. N. Akhmediev, V.M. Eleonoskii, and N.E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894 (1985).

W. Chen, Z. Song, and Z. Meng, “Periodical spectral holes along fiber dispersion at the second-order modulation instability sideband,” Opt. Quantum Electron. 47, 3427–3434 (2015).

[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–115 (2011).

[Crossref]
[PubMed]

E. Seve, G. Millot, and S. Trillo, “Strong four-photon conversion regime of cross-phase modulation induced modulational instability,” Phys. Rev. E. 61, 3139–3150 (2000).

[Crossref]

G. Millot, E. Seve, S. Wabnitz, and S. Trillo, “Observation of a novel large-signal four-photon instability in optical wave mixing,” Phys. Rev. Lett. 80, 504–507 (1998).

[Crossref]

S. Trillo, G. Millot, E. Seve, and S. Wabnitz, “Failure of phase matching concept in large-signal parametric frequency conversion,” Appl. Phys. Lett. 72, 150–152 (1997).

[Crossref]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).

[Crossref]

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4, 011054 (2014).

A. Bendahmane, A. Mussot, P. Szriftgiser, O. Zerkak, G. Genty, J. M. Dudley, and A. Kudlinski, “Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber,” Opt. Lett. 39, 4490–4493 (2011).

[Crossref]

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 18, 11185 (2007).

[Crossref]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).

[Crossref]

A. Osborne, “The random and deterministic dynamics of rogue waves in unidirectional, deep-water wave trains,” Marine structures 14, 275–293 (2001).

[Crossref]

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238, 540–548 (2009).

[Crossref]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).

[Crossref]

A. Vedenov and L. I. Rudakov, “Interaction of waves in continuous media,” Sov. Phys. Dokl. 9, 1073 (1965).

A. Calini and C. M. Schober, “Homoclinic chaos increases the likelihood of rogue wave formation,” Phys. Lett. A. 298, 335–349 (2000).

[Crossref]

M. J. Ablowitz, J. Hammack, D. Henderson, and C.M. Schober, “Modulated periodic Stokes waves in deep water,” Phys. Rev. Lett. 84, 887–890 (2000).

[Crossref]
[PubMed]

E. Seve, G. Millot, and S. Trillo, “Strong four-photon conversion regime of cross-phase modulation induced modulational instability,” Phys. Rev. E. 61, 3139–3150 (2000).

[Crossref]

G. Millot, E. Seve, S. Wabnitz, and S. Trillo, “Observation of a novel large-signal four-photon instability in optical wave mixing,” Phys. Rev. Lett. 80, 504–507 (1998).

[Crossref]

S. Trillo, G. Millot, E. Seve, and S. Wabnitz, “Failure of phase matching concept in large-signal parametric frequency conversion,” Appl. Phys. Lett. 72, 150–152 (1997).

[Crossref]

W. Chen, Z. Song, and Z. Meng, “Periodical spectral holes along fiber dispersion at the second-order modulation instability sideband,” Opt. Quantum Electron. 47, 3427–3434 (2015).

[Crossref]

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4, 011054 (2014).

A. Bendahmane, A. Mussot, P. Szriftgiser, O. Zerkak, G. Genty, J. M. Dudley, and A. Kudlinski, “Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber,” Opt. Lett. 39, 4490–4493 (2011).

[Crossref]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[Crossref]
[PubMed]

V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307 (1966).

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[Crossref]
[PubMed]

E. Seve, G. Millot, and S. Trillo, “Strong four-photon conversion regime of cross-phase modulation induced modulational instability,” Phys. Rev. E. 61, 3139–3150 (2000).

[Crossref]

G. Millot, E. Seve, S. Wabnitz, and S. Trillo, “Observation of a novel large-signal four-photon instability in optical wave mixing,” Phys. Rev. Lett. 80, 504–507 (1998).

[Crossref]

S. Trillo, G. Millot, E. Seve, and S. Wabnitz, “Failure of phase matching concept in large-signal parametric frequency conversion,” Appl. Phys. Lett. 72, 150–152 (1997).

[Crossref]

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B. 8, 824–840 (1991).

[Crossref]

S. Trillo and S. Wabnitz, “Self-injected spatial mode locking and coherent all-optical FM/AM switching based on modulational instability,” Opt. Lett. 16, 1566–1568 (1991)

[Crossref]
[PubMed]

G. Cappellini and S. Trillo, “Energy conversion in degenerate four-photon mixing in birefringent fibers,” Opt. Lett. 16, 895–897 (1991).

[Crossref]
[PubMed]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16, 986–988 (1991).

[Crossref]
[PubMed]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B. 3, 477–486 (2002).

[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[Crossref]
[PubMed]

A. Vedenov and L. I. Rudakov, “Interaction of waves in continuous media,” Sov. Phys. Dokl. 9, 1073 (1965).

S. Wabnitz and N. Akhmediev, “Efficient modulation frequency doubling by induced modulation instability,” Opt. Commun. 283, 1152–1154 (2010).

[Crossref]

G. Millot, E. Seve, S. Wabnitz, and S. Trillo, “Observation of a novel large-signal four-photon instability in optical wave mixing,” Phys. Rev. Lett. 80, 504–507 (1998).

[Crossref]

S. Trillo, G. Millot, E. Seve, and S. Wabnitz, “Failure of phase matching concept in large-signal parametric frequency conversion,” Appl. Phys. Lett. 72, 150–152 (1997).

[Crossref]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16, 986–988 (1991).

[Crossref]
[PubMed]

S. Trillo and S. Wabnitz, “Self-injected spatial mode locking and coherent all-optical FM/AM switching based on modulational instability,” Opt. Lett. 16, 1566–1568 (1991)

[Crossref]
[PubMed]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375, 2029 (2011).

[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

H. C. Yuen and W. E. Ferguson, “Relationship between Benjamin-Feir instability and recurrence in the nonlinear Schrödinger equation,” Phys. Fluids 21, 1275 (1978).

[Crossref]

V. E. Zakharov and A. A. Gelash, “Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability,” Nonlinearity 27, R1–R39 (2014).

[Crossref]

V. E. Zakharov and A. A. Gelash, “Nonlinear stage of modulation instability,” Phys. Rev. Lett. 111, 054101 (2013).

[Crossref]
[PubMed]

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238, 540–548 (2009).

[Crossref]

S. Trillo, G. Millot, E. Seve, and S. Wabnitz, “Failure of phase matching concept in large-signal parametric frequency conversion,” Appl. Phys. Lett. 72, 150–152 (1997).

[Crossref]

T. B. Benjamin and J. E. Feir, “The disintegration of wavetrains on deep water. Part 1: Theory,” J. Fluid Mech. 27, 417–430 (1967).

[Crossref]

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B. 8, 824–840 (1991).

[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B. 3, 477–486 (2002).

[Crossref]

V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307 (1966).

A. Osborne, “The random and deterministic dynamics of rogue waves in unidirectional, deep-water wave trains,” Marine structures 14, 275–293 (2001).

[Crossref]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photonics 8, 755–764 (2014).

[Crossref]

V. E. Zakharov and A. A. Gelash, “Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability,” Nonlinearity 27, R1–R39 (2014).

[Crossref]

S. Wabnitz and N. Akhmediev, “Efficient modulation frequency doubling by induced modulation instability,” Opt. Commun. 283, 1152–1154 (2010).

[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Exp. 17, 21497–21508 (2009).

[Crossref]

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 18, 11185 (2007).

[Crossref]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–115 (2011).

[Crossref]
[PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2143 (2011).

[Crossref]
[PubMed]

A. Bendahmane, A. Mussot, P. Szriftgiser, O. Zerkak, G. Genty, J. M. Dudley, and A. Kudlinski, “Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber,” Opt. Lett. 39, 4490–4493 (2011).

[Crossref]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16, 986–988 (1991).

[Crossref]
[PubMed]

S. Trillo and S. Wabnitz, “Self-injected spatial mode locking and coherent all-optical FM/AM switching based on modulational instability,” Opt. Lett. 16, 1566–1568 (1991)

[Crossref]
[PubMed]

M. E. Marhic, K. K. Y. Wong, M. C. Ho, and L. G. Kazovsky, “92% Pump depletion in a continuous-wave one-pump fiber optical parametric amplifier,” Opt. Lett. 26, 620–622 (2001).

[Crossref]

G. Cappellini and S. Trillo, “Energy conversion in degenerate four-photon mixing in birefringent fibers,” Opt. Lett. 16, 895–897 (1991).

[Crossref]
[PubMed]

W. Chen, Z. Song, and Z. Meng, “Periodical spectral holes along fiber dispersion at the second-order modulation instability sideband,” Opt. Quantum Electron. 47, 3427–3434 (2015).

[Crossref]

H. C. Yuen and W. E. Ferguson, “Relationship between Benjamin-Feir instability and recurrence in the nonlinear Schrödinger equation,” Phys. Fluids 21, 1275 (1978).

[Crossref]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375, 2029 (2011).

[Crossref]

A. Calini and C. M. Schober, “Homoclinic chaos increases the likelihood of rogue wave formation,” Phys. Lett. A. 298, 335–349 (2000).

[Crossref]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).

[Crossref]

E. Seve, G. Millot, and S. Trillo, “Strong four-photon conversion regime of cross-phase modulation induced modulational instability,” Phys. Rev. E. 61, 3139–3150 (2000).

[Crossref]

G. Millot, E. Seve, S. Wabnitz, and S. Trillo, “Observation of a novel large-signal four-photon instability in optical wave mixing,” Phys. Rev. Lett. 80, 504–507 (1998).

[Crossref]

M. J. Ablowitz, J. Hammack, D. Henderson, and C.M. Schober, “Modulated periodic Stokes waves in deep water,” Phys. Rev. Lett. 84, 887–890 (2000).

[Crossref]
[PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[Crossref]
[PubMed]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107, 253901 (2011).

[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[Crossref]
[PubMed]

V. E. Zakharov and A. A. Gelash, “Nonlinear stage of modulation instability,” Phys. Rev. Lett. 111, 054101 (2013).

[Crossref]
[PubMed]

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4, 011054 (2014).

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238, 540–548 (2009).

[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[Crossref]

M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM J. Appl. Math. 50, 339–351 (1990).

[Crossref]

G. Biondini and E. Fagerstrom, “The integrable nature of modulational instability,” SIAM J. Appl. Math. 75, 136–163 (2015).

[Crossref]

A. Vedenov and L. I. Rudakov, “Interaction of waves in continuous media,” Sov. Phys. Dokl. 9, 1073 (1965).

N. N. Akhmediev, V.M. Eleonoskii, and N.E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894 (1985).

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 69, 1089–1093 (1987).

[Crossref]