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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A family of wave equations with some remarkable properties

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Author(s):
da Silva, Priscila Leal [1] ; Freire, Igor Leite [2] ; Santos Sampaio, Julio Cesar [3]
Total Authors: 3
Affiliation:
[1] Univ Fed Sao Carlos, Dept Matemat, Sao Carlos, SP - Brazil
[2] UFABC Santo Andre, Ctr Matemat Comp & Cognicao, Santo Andre, SP - Brazil
[3] Univ Metodista Sao Paulo UMESP, Sao Bernardo Do Campo - Brazil
Total Affiliations: 3
Document type: Journal article
Source: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SC; v. 474, n. 2210 FEB 2018.
Web of Science Citations: 0
Abstract

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrodinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation. (AU)

FAPESP's process: 11/23538-0 - Ibragimov's theorem and conservation laws for equations without Lagrangians.
Grantee:Júlio Cesar Santos Sampaio
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 14/05024-8 - Symmetries and conservation laws for differential equations arising from physical and biological systems
Grantee:Igor Leite Freire
Support Opportunities: Regular Research Grants
FAPESP's process: 12/22725-4 - Invariance properties and conserved quantities: Noether's theorem and Ibragimov's theorem
Grantee:Priscila Leal da Silva
Support Opportunities: Scholarships in Brazil - Master