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Invariant Subspace Classification and Exact Explicit Solutions to a Class of Nonlinear Wave Equation

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Abstract

In this paper, the invariant subspace classification of a class of nonlinear shallow water wave equation is given, then some exact explicit solutions to the nonlinear equation are provided by using the invariant subspace method. This method is a dynamical system method by nature, for its key step is to transform a nonlinear partial differential equation (PDE) into ordinary differential equation (ODE) systems, then by solving the ODE systems, the exact solutions to the nonlinear PDE are obtained.

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Acknowledgements

The authors would like to thank the Editor an Reviewers for their valuable comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, Shandong, China

    Lina Chang, Hanze Liu & Xiangpeng Xin

Authors
  1. Lina Chang
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  2. Hanze Liu
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  3. Xiangpeng Xin
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Correspondence to Hanze Liu.

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This work was supported by the National Natural Science Foundation of China under Grant Nos. 11171041 and 11505090, the high-level personnel foundation of Liaocheng University under Grant Nos. 31805 and 318011613.

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Chang, L., Liu, H. & Xin, X. Invariant Subspace Classification and Exact Explicit Solutions to a Class of Nonlinear Wave Equation. Qual. Theory Dyn. Syst. 19, 65 (2020). https://doi.org/10.1007/s12346-020-00400-6

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