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On asymptotic stability of kink for relativistic Ginzburg-Landau equations. (English) Zbl 1256.35146

Summary: We prove the asymptotic stability of kink for the nonlinear relativistic wave equations of the Ginzburg-Landau type in one space dimension: for any odd initial condition in a small neighborhood of the kink, the solution, asymptotically in time, is the sum of the kink and dispersive part described by the free Klein-Gordon equation. The remainder converges to zero in a global norm.

MSC:

35Q56 Ginzburg-Landau equations
35Q75 PDEs in connection with relativity and gravitational theory
83A05 Special relativity
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