Pseudorecurrence and chaos of cubic-quintic nonlinear Schrödinger equation

Abstract

Recurrence, pseudorecurrence, and chaotic solutions for a continuum Hamiltonian system in which there exist spatial patterns of solitary wave structures are investigated using the nonlinear Schrödinger equation (NSE) with cubic and quintic terms. The theoretical analyses indicate that there may exist Birkhoff's recurrence for the arbitrary parameter values. The numerical experiments show that there may be Fermi-Pasta-Ulam (FPU) recurrence, pseudorecurrence, and chaos when different initial conditions are chosen. The fact that the system energy is effectively shared by finite Fourier modes suggests that it may be possible to describe the continuum system in terms of some effective degrees of freedom.