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

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Published 12 February 2018 • © 2018 IOP Publishing Ltd & London Mathematical Society
, , Citation João-Paulo Dias and Pedro Freitas 2018 Nonlinearity 31 1110 DOI 10.1088/1361-6544/aaaa09

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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

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4 Author to whom any correspondence should be addressed.

Dates

  1. Received 12 September 2017
  2. Accepted 23 January 2018
  3. Published

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0951-7715/31/3/1110

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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10.1088/1361-6544/aaaa09