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Decay of solutions for a class of nonlinear Schrödinger equations in \(\mathbb{R}\) and the stability of shock profiles for a quasilinear Benney system. (English) Zbl 1390.35322

Summary: We study the stability in a partial linearisation framework of a particular travelling wave \((0,\tilde{V})\) of the quasilinear Benney system, where \( \tilde{V}\) is a standing wave with a shock profile for the viscous conservation law.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B35 Stability in context of PDEs
35C07 Traveling wave solutions
35C20 Asymptotic expansions of solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
76L05 Shock waves and blast waves in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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References:

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