On asymptotic stability of moving kink for relativistic Ginzburg-Landau equation

Abstract

We prove the asymptotic stability of the moving kinks for the nonlinear relativistic wave equations in one space dimension with a Ginzburg-Landau potential: starting in a small neighborhood of the kink, the solution, asymptotically in time, is the sum of a uniformly moving kink and dispersive part described by the free Klein-Gordon equation. The remainder decays in a global energy norm. Crucial role in the proofs play our recent results on the weighted energy decay for the Klein-Gordon equations.

30 pages, 0 figures

References in corpus (2)

• On asymptotic stability in energy space of ground states for Nonlinear Schrödinger equations
• On the asymptotic stability of bound states in 2D cubic Schroedinger equation

Cited by in corpus (4)

• On eigenfunction expansion of solutions to the Hamilton equations
• On asymptotic stability of solitons for nonlinear Schödinger equation
• Attractors of nonlinear Hamiltonian PDEs
• On the eigenfunction expansion for the Hamilton operators