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Conservation laws and integral relations for the Boussinesq equation

Citation

Ankiewicz, A and Bassom, AP and Clarkson, PA and Dowie, E, Conservation laws and integral relations for the Boussinesq equation, Studies in Applied Mathematics, 139, (1) pp. 104-128. ISSN 0022-2526 (2017) [Refereed Article]

Copyright Statement

Copyright 2017 Wiley Periodicals, Inc.

DOI: doi:10.1111/sapm.12174

Abstract

We are concerned with conservation laws and integral relations associated with rational solutions of the Boussinesq equation, a soliton equation solvable by inverse scattering, which was first introduced by Boussinesq in 1871. The rational solutions are logarithmic derivatives of a polynomial, are algebraically decaying, and have a similar appearance to rogue-wave solutions of the focusing nonlinear Schrödinger equation. For these rational solutions, the constants of motion associated with the conserved quantities are zero and they have some interesting integral relations, which depend on the total degree of the associated polynomial.

Item Details

Item Type:Refereed Article
Keywords:conservation laws, Boussinesq equation
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:118286
Year Published:2017
Web of Science® Times Cited:3
Deposited By:Mathematics and Physics
Deposited On:2017-07-10
Last Modified:2018-04-27
Downloads:0

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