Abstract

Numerical solutions of a nonlinear Schrödinger equation may suffer from the spurious four-wave mixing processes. We study how these nonphysical resonances appear in solutions of a much more stiff generalized nonlinear Schrödinger equation with an arbitrary dispersion operator and determine the necessary restrictions on temporal and spatial resolution of a numerical scheme. The restrictions are especially important to meet when an envelope equation has to be applied in a wide spectral window, e.g., because of the spectral broadening.

Idealized four-wave mixing dynamics in a nonlinear Schrödinger equation fiber system

Anastasiia Sheveleva, Ugo Andral, Bertrand Kibler, Pierre Colman, John M. Dudley, and Christophe Finot
Optica 9(6) 656-662 (2022)

Mode profile dispersion in the generalized nonlinear Schrödinger equation

J. Lægsgaard
Opt. Express 15(24) 16110-16123 (2007)

Photon-conserving generalized nonlinear Schrödinger equation for frequency-dependent nonlinearities

J. Bonetti, N. Linale, A. D. Sánchez, S. M. Hernandez, P. I. Fierens, and D. F. Grosz
J. Opt. Soc. Am. B 37(2) 445-450 (2020)

Generation of random soliton-like beams in a nonlinear fractional Schrödinger equation

Juanfen Wang, Yuan Jin, Xuguang Gong, Lingzhen Yang, Jie Chen, and Pingping Xue
Opt. Express 30(5) 8199-8211 (2022)

Rogue wave light bullets of the three-dimensional inhomogeneous nonlinear Schrödinger equation

Jingsong He, Yufeng Song, C. G. L. Tiofack, and M. Taki
Photon. Res. 9(4) 643-648 (2021)