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The traveling wave solutions for a two-component b-family equations

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Abstract

Solitary wave solution and peakon solution are of great significance to the study of the water wave equation. These solutions are also called traveling wave solutions. This work is devoted to investigating a class of traveling wave solutions of a two-component b-family equations. We first give the definition of the weak solutions of the equations. By virtue of the x-symmetry of the solutions and the uniqueness of the weak solutions, then we prove that the equations has a family of traveling wave solutions.

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Acknowledgements

This work was partially supported by NSFC (Grant No.: 11771442, 11971042) and the Fundamental Research Funds for the Central University (WUT: 2021III056JC). The authors thank the professor Boling Guo and Zhen Wang for their helpful discussions and constructive suggestions.

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  1. Center for Mathematical Sciences, School of Science, Wuhan University of Technology, Wuhan, 430070, People’s Republic of China

    Lijun Du & Xinglong Wu

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  1. Lijun Du
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  2. Xinglong Wu
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Correspondence to Lijun Du.

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Communicated by Adrian Constantin.

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Du, L., Wu, X. The traveling wave solutions for a two-component b-family equations. Monatsh Math 202, 741–750 (2023). https://doi.org/10.1007/s00605-023-01865-8

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