Clarkson, Peter and Dowie, Ellen (2016) Rational solutions of the Boussinesq equation and applications to rogue waves. Technical report. arxiv.org (KAR id:59906)
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Official URL: https://arxiv.org/abs/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: | Monograph (Technical report) |
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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: | 16 Feb 2021 13:41 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/59906 (The current URI for this page, for reference purposes) |
Clarkson, Peter: | ![]() |
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