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

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 56, n. 9 SEP 2015.
• Web of Science Citations: 10

Abstract

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)

• 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
• 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