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arXiv · 1412.4415

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

Stephen C. Anco·Priscila Leal da Silva·Igor Leite Freire
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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 $N=2$.

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Stephen C. Anco, Priscila Leal da Silva, Igor Leite Freire. 2015-07-18. A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations. https://doi.org/10.1063/1.4929661

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