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 |
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| Resource title: | Rational solutions of the Boussinesq equation and applications to rogue waves |
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| Resource type: | Publication |
| DOI: | 10.1093/imatrm/tnx003 |
| KDR/KAR URL: | https://kar.kent.ac.uk/64073 |
| External URL: | https://doi.org/10.1093/imatrm/tnx003 |
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 |
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| 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: | 05 Nov 2024 10:52 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/59906 (The current URI for this page, for reference purposes) |
University of Kent Author Information
Clarkson, Peter.
| Creator's ORCID: |
 https://orcid.org/0000-0002-8777-5284
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| CReDIT Contributor Roles: |
Dowie, Ellen.
| Creator's ORCID: |
https://orcid.org/0000-0001-5527-4656
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| CReDIT Contributor Roles: |
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