A family of wave equations with some remarkable properties

Autor(es)

da Silva, Priscila Leal ^[1] ; Freire, Igor Leite ^[2] ; Santos Sampaio, Julio Cesar ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SC; v. 474, n. 2210 FEB 2018.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 11/23538-0 - O Teorema de Ibragimov e leis de conservação de equações diferenciais sem Lagrageanas.
• Beneficiário: Júlio Cesar Santos Sampaio
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 14/05024-8 - Simetrias e leis de conservação de equações diferenciais oriundas de sistemas físicos e biológicos
• Beneficiário: Igor Leite Freire
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 12/22725-4 - Propriedades de invariância e quantidades conservadas: o Teorema de Noether e o Teorema de Ibragimov
• Beneficiário: Priscila Leal da Silva
• Modalidade de apoio: Bolsas no Brasil - Mestrado