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Rational solutions of the Boussinesq equation and applications to rogue waves

Clarkson, Peter and Dowie, Ellen (2017) Rational solutions of the Boussinesq equation and applications to rogue waves. [Preprint] (doi:10.48550/arXiv.1609.00503) (KAR id:59906)

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Official URL:
https://doi.org/10.48550/arXiv.1609.00503

Abstract

We study rational solutions of the Boussinesq equation, which is a soliton equation solvable by the inverse scattering method. These rational solutions, which are algebraically decaying and depend on two arbitrary parameters, are expressed in terms of special polynomials that are derived through a bilinear equation, have a similar appearance to rogue-wave solutions of the focusing nonlinear Schr\"{o}dinger (NLS) equation and have an interesting structure. Further rational solutions of the Kadomtsev-Petviashvili I (KPI) equation are derived in two ways, from rational solutions of the NLS equation and from rational solutions of the Boussinesq equation. It is shown that the two families of rational solutions of the KPI equation are fundamentally different.

Item Type: Preprint
DOI/Identification number: 10.48550/arXiv.1609.00503
Refereed: No
Other identifier: https://arxiv.org/abs/1609.00503
Name of pre-print platform: arXiv
Subjects: Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Peter Clarkson
Date Deposited: 18 Jan 2017 06:12 UTC
Last Modified: 17 Oct 2023 03:11 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/59906 (The current URI for this page, for reference purposes)

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