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Conservation laws and integral relations for the Boussinesq equation
journal contribution
posted on 2023-05-19, 07:08 authored by Ankiewicz, A, Andrew BassomAndrew Bassom, Clarkson, PA, Dowie, EWe 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.
History
Publication title
Studies in Applied MathematicsVolume
139Pagination
104-128ISSN
0022-2526Department/School
School of Natural SciencesPublisher
Blackwell PublishersPlace of publication
350 Main Street, Ste 6, Malden, USA, Ma, 02148Rights statement
Copyright 2017 Wiley Periodicals, Inc.Repository Status
- Restricted