Decay of solutions for a class of nonlinear Schrödinger equations in $ \newcommand{\R}{\mathbb{R}} \R$ and the stability of shock profiles for a quasilinear Benney system

DOI10.1088/1361-6544/AAAA09zbMath1390.35322OpenAlexW2793339672MaRDI QIDQ4635066

Pedro Freitas, João-Paulo Dias

Publication date: 13 April 2018

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/aaaa09

zbMATH Keywords

stabilitynonlinear Schrödinger equationstanding waveBenney system

Mathematics Subject Classification ID

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

Related Items (1)

Linear stability of shock profiles for a quasilinear Benney system in ℝ2 × ℝ+

Cites Work

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• Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion
• Existence of local strong solutions for a quasilinear Benney system
• Vanishing viscosity with short wave-long wave interactions for systems of conservation laws
• Sharp asymptotic behavior of solutions for cubic nonlinear Schrödinger equations with a potential
• EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS
• A General Theory for Interactions Between Short and Long Waves
• Decay and Scattering of Small Solutions of Pure Power NLS in ℝ with p > 3 and with a Potential

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