Decay of solutions for a class of nonlinear Schrödinger equations in  and the stability of shock profiles for a quasilinear Benney system

João-Paulo Dias; Pedro Freitas

doi:10.1088/1361-6544/aaaa09

Nonlinearity

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Paper

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

João-Paulo Dias¹ and Pedro Freitas^2,3,4

Published 12 February 2018 • © 2018 IOP Publishing Ltd & London Mathematical Society
Nonlinearity, Volume 31, Number 3

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Author e-mails

jpdias@fc.ul.pt

psfreitas@fc.ul.pt

Author affiliations

¹ CMAF-CIO and Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016 Lisboa, Portugal

² Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

³ Grupo de Física Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016 Lisboa, Portugal

⁴ Author to whom any correspondence should be addressed.

Dates

Received 12 September 2017
Accepted 23 January 2018
Published 12 February 2018

Citation

João-Paulo Dias and Pedro Freitas 2018 Nonlinearity 31 1110

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DOI

https://doi.org/10.1088/1361-6544/aaaa09

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Abstract

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

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