A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations

Autor(es)

Anco, Stephen C. ^[1] ; da Silva, Priscila Leal ^[2] ; Freire, Igor Leite ^[2]

Afiliação do(s) autor(es)

^[1] Brock Univ, Dept Math & Stat, St Catharines, ON L2S 3A1 - Canada

^[2] Univ Fed ABC, Ctr Matemat Comp & Cognicao, BR-09210580 Santo Andre, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 56, n. 9 SEP 2015.
• Citações Web of Science: 10

Resumo

A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov equations that describe breaking waves is introduced. A classification of low-order conservation laws, peaked travelling wave solutions, and Lie symmetries is presented for this family. These classifications pick out a 1-parameter equation that has several interesting features: it reduces to the Camassa-Holm and Novikov equations when the polynomial has degree two and three; it has a conserved H-1 norm and it possesses N-peakon solutions when the polynomial has any degree; and it exhibits wave-breaking for certain solutions describing collisions between peakons and anti-peakons in the case N = 2. (C) 2015 AIP Publishing LLC. (AU)

• 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
• 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