Pattern Formation and Competition in the Regime of the Conserved Cubic-Quintic Nonlinear Schrödinger Equation

Abstract

In this letter, the pattern formation, pattern competition and spatiotemporal chaos are first investigated in the regime of cubic-quintic nonlinear Schrödinger equation in a near-integrable Hamiltonian continuum system using a few important representative manifolds in phase space. We find that the regular pattern competition can exist in some regions of the controlled parameters, and the spatiotemporal chaos may result from stochastic competition of the patterns. This conclusion may be generalized to the systems which have the saddle structure.