PSEUDORECURRENCE AND CHAOS OF CUBIC-QUINTIC NONLINEAR SCHRODINGER-EQUATION

Recurrence, pseudorecurrence, and chaotic solutions for a continuum Ha miltonian system in which there exist spatial patterns of solitary wav e structures are investigated using the nonlinear Schrodinger equation (NSE) with cubic and quintic terms. The theoretical analyses indicate that there may exist Birkhoff's recurrence for the arbitrary paramete r values. The numerical experiments show that there may be Fermi-Pasta -Ulam (FPU) recurrence, pseudorecurrence, and chaos when different ini tial conditions are chosen. The fact that the system energy is effecti vely shared by finite Fourier modes suggests that it may be possible t o describe the continuum system in terms of some effective degrees of freedom.