Solitary waves for an internal wave model

José Raúl Quintero; Juan Carlos Muñoz  Grajales

doi:10.3934/dcds.2016051

Article Contents

2016, Volume 36, Issue 10: 5721-5741. Doi: 10.3934/dcds.2016051

This issue Previous Article Matsaev's type theorems for solutions of the stationary Schrödinger equation and its applications Next Article The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension

Solitary waves for an internal wave model

José Raúl Quintero^1, and
Juan Carlos Muñoz Grajales^1,

1.
Departamento de Matemáticas, Universidad del Valle, Calle 13 Nro. 100-00, Cali

Received: July 31, 2015

Revised: March 31, 2016

Published: May 2017

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Abstract

We show the existence of solitary wave solutions of finite energy for a model to describe the propagation of internal waves for wave speed $c$ large enough. Furthermore, some of these solutions are approximated using a Newton-type iteration combined with a collocation-spectral strategy for spatial discretization of the corresponding solitary wave equations.

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Mathematics Subject Classification: Primary: 74J35, 35A01, 65M70; Secondary: 37C25, 35Q51, 35Q35.

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