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On asymptotic stability of moving kink for relativistic Ginzburg-Landau equation. (English) Zbl 1209.35134

Summary: 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. Our recent results on the weighted energy decay for the Klein-Gordon equations play a crucial role in the proofs.

MSC:

35Q56 Ginzburg-Landau equations
35Q75 PDEs in connection with relativity and gravitational theory
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35C08 Soliton solutions
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