A simple criterion of transverse linear instability for solitary waves

2009/10/20 by Rousset, F., Tzvetkov, N. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.0910.3789

Abstract

We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various examples from mathematical physics.

Cited by

• Numerical study of transverse (in-)stability of solitary waves in the cubic-quintic nonlinear Schrödinger equation

Related

• Transverse instability of the line solitary water-waves
• Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's
• Transverse nonlinear instability for two-dimensional dispersive models
• Transverse instability of the CH-KP-I equation
• Transverse instability for nonlinear Schrödinger equation with a linear potential