Large scale instability of nonlinear standing waves

Large scale instability of nonlinear standing waves

Strong Instability of Standing Waves for Nonlinear Klein-gordon Equations

The strong instability of ground state standing wave solutions eφω(x) for nonlinear Klein-Gordon equations has been known only for the case ω = 0. In this paper we prove the strong instability for small frequency ω.

Stability and instability of standing waves for nonlinear Schrödinger equations

An Instability Criterion for Nonlinear Standing Waves on Nonzero Backgrounds

In this work, we study the standing wave solutions of an inhomogeneous nonlinear Schrödinger equation. The inhomogeneity considered here is a varying coefficient of the nonlinear term. In particular, the nonlinearity is chosen to be repelling (defocusing) except on a finite interval. Localized solutions on a nonzero background, e.g., dark solitons trapped by the inhomogeneity, are identified an...

Nonlinear Counterpropagating Waves, Multisymplectic Geometry, and the Instability of Standing Waves

Standing waves are a fundamental class of solutions of nonlinear wave equations with a spatial reflection symmetry, and they routinely arise in optical and oceanographic applications. At the linear level they are composed of two synchronized counterpropagating periodic traveling waves. At the nonlinear level, they can be defined abstractly by their symmetry properties. In this paper, general as...