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Multiple-soliton and periodic solutions to space–time fractional Whitham–Broer–Kaup equations

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Abstract

In this paper, the space–time fractional Whitham–Broer–Kaup equations are investigated. By means of new fractional scaling transformations, the fractional nonlinear system of different time and space orders is transformed to the integer one. The multiple solitary solutions and periodic solutions are obtained, respectively. All those solutions are given exactly by introducing new scaling transformations, which makes our study unique and different from most existing studies. It is expected that exact solutions for nonlinear wave system of fractional order can be handled in the similar way.

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Data availability statement

The data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (Approval Nos. 11872241, 12062018 and 12172333), Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Approval No. NJYT22075) and the Natural Science Foundation of Inner Mongolia (Approval No. 2020MS01015).

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Authors and Affiliations

  1. State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Hang Xu

  2. College of Science, Inner Mongolia University of Technology, Hohhot, 010051, China

    Wenhao Cheng & Jifeng Cui

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  1. Hang Xu
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  2. Wenhao Cheng
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  3. Jifeng Cui
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Correspondence to Jifeng Cui.

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Xu, H., Cheng, W. & Cui, J. Multiple-soliton and periodic solutions to space–time fractional Whitham–Broer–Kaup equations. Eur. Phys. J. Spec. Top. 231, 2353–2357 (2022). https://doi.org/10.1140/epjs/s11734-021-00374-9

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