Conservation Laws and Integral Relations for the Boussinesq Equation

A. Ankiewicz; A. P. Bassom; P. A. Clarkson; E. Dowie

doi:10.1111/sapm.12174

Conservation Laws and Integral Relations for the Boussinesq Equation

A. Ankiewicz, A. P. Bassom, P. A. Clarkson^*, E. Dowie

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

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.

Original language	English
Pages (from-to)	104-128
Number of pages	25
Journal	Studies in Applied Mathematics
Volume	139
Issue number	1
DOIs	https://doi.org/10.1111/sapm.12174
Publication status	Published - Jul 2017

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Conservation Laws and Integral Relations for the Boussinesq Equation

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