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arXiv · 1811.05843

Existence of peakons for a cubic generalization of the Camassa-Holm equation

Yun Wang·Lixin Tian
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Abstract

In this paper, we study the following generalized Camassa-Holm equation with both cubic and quadratic nonlinearities: $$ m_{t}+k_{1}(3uu_{x}m+u^2m_{x})+k_{2}(2mu_{x}+m_{x}u)=0, \quad m=u-u_{xx}, $$ which is presented as a linear combination of the Novikov equation and the Camassa-Holm equation with constants $k_{1}$ and $k_{2}$. The model is a cubic generalization of the Camassa-Holm equation. It is shown that the equation admits single-peaked soliton and periodic peakons.

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Yun Wang, Lixin Tian. 2018-11-14. Existence of peakons for a cubic generalization of the Camassa-Holm equation. https://arxiv.org/abs/1811.05843

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