Advances in Differential Equations

On the existence of solitary waves for Boussinesq type equations and Cauchy problem for a new conservative model

Stevan Bellec and Mathieu Colin

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Abstract

In this paper, we present a long time existence theory for a new enhanced Boussinesq-Type system with constant bathymetry written in a conservative form. We also prove the existence of solitary wave for a large class of asymptotic models, including Beji-Nadaoka, Madsen-Sorensen and Nwogu equations. Furthermore, we give a procedure to calculate numerically these particular solutions and we present some effective computations.

Article information

Source
Adv. Differential Equations Volume 21, Number 9/10 (2016), 945-976.

Dates
First available in Project Euclid: 14 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ade/1465912587

Mathematical Reviews number (MathSciNet)
MR3513122

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 35A01: Existence problems: global existence, local existence, non-existence 35C07: Traveling wave solutions

Citation

Bellec, Stevan; Colin, Mathieu. On the existence of solitary waves for Boussinesq type equations and Cauchy problem for a new conservative model. Adv. Differential Equations 21 (2016), no. 9/10, 945--976. https://projecteuclid.org/euclid.ade/1465912587.


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