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Conservation Laws and Integral Relations for the Boussinesq Equation

Ankiewicz, Adrian, Bassom, Andrew P., Clarkson, Peter, Dowie, Ellen (2017) Conservation Laws and Integral Relations for the Boussinesq Equation. Studies in Applied Mathematics, 139 (1). pp. 104-128. ISSN 0022-2526. E-ISSN 1467-9590. (doi:10.1111/sapm.12174) (KAR id:61648)

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https://dx.doi.org/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 Type: Article
DOI/Identification number: 10.1111/sapm.12174
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Peter Clarkson
Date Deposited: 08 May 2017 15:11 UTC
Last Modified: 16 Feb 2021 13:45 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/61648 (The current URI for this page, for reference purposes)
Clarkson, Peter: https://orcid.org/0000-0002-8777-5284
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