Abstract

In nonequilibrium nonlinear systems the problem of the growth of spatial domains of different phases is, in general, poorly understood. For example, several exponents have been given for the growth of domains made of equivalent phases in nonlinear optical systems, including R(t) ≈ t^1/2 [1,2] and R(t) ≈ t^1/3 [3], but there is a lack of understanding of the dynamical mechanism giving rise to the observed scaling laws. Furthermore in some regimes the dynamics of domain growth may be linked to the dynamics of formation of localized structures and labyrinthine patterns, also observed in this systems [1,2]. Here we will demonstrate that a rather general class of nonlinear systems, included OPO and vectorial Kerr cavity, which have bistability between two equivalent homogeneous solutions displays the following scenario: For a range of values of a control parameter p > p_c there is a flat Ising front connecting the two homogeneous states is stable. In this regime a domain of one solution embedded in the other shrinks as $R(t)=\sqrt{R(t=0)-\gamma t}$ and a coarsening regime with t¹/² growth law is observed. If the front connecting the two homogeneous states has oscillatory tails, they can prevent the collapse of the droplet and a soliton-like localized structure is formed. In many of these systems there is a critical value of the control parameter p_c for which the flat wall becomes modulationally unstable.

© 2001 EPS