Global bifurcation of traveling waves in discrete nonlinear Schrödinger equations

Abstract

We consider discrete nonlinear Schrödinger equations of n sites with periodic boundary conditions. These equations have n branches of standing waves that bifurcate from zero. Traveling waves appear as a symmetry-breaking from the standing waves for different amplitudes. The bifurcation is proved using the global Rabinowitz alternative in subspaces of symmetric functions. As examples, we present applications to the Schrödinger and Saturable lattices.

Cited by in corpus (1)

• Choreographies in the Discrete Nonlinear Schrödinger Equations