Global bifurcation of traveling waves in discrete nonlinear Schrödinger equations

2015/08/04 by Carlos García-Azpeitia, García-Azpeitia, Carlos
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1508.00832

arxiv created 2016/04/26 · arxiv updated 2016/04/27

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.

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