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Solitary Waves and Periodic Waves in a Perturbed KdV Equation

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Abstract

In this paper, we consider a perturbed Korteweg–de Vries (KdV) equation with weak dissipation and Marangoni effects. Main attention is focused on the existence conditions of periodic and solitary wave solutions of the perturbed KdV equation. Based on bifurcation theory of dynamic system and geometric singular perturbation method, the parameter conditions and wave speed conditions for the existence of one periodic solution, one solitary solution and the coexistence of a solitary solution and infinite number of periodic solutions are given. By using Chebyshev criterion to analyze the ratio of Abelian integrals, the monotonicity of wave speed is proved, and the upper and lower bounds of wave speed are obtained.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (11661046, 11901547).

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Authors and Affiliations

  1. Department of Mathematics, Jiujiang University, Jiujiang, 332005, People’s Republic of China

    Hong Li & Hongquan Sun

  2. Department of Mathematics, China Jiliang University, Hangzhou, 310018, People’s Republic of China

    Wenjing Zhu

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  1. Hong Li
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Correspondence to Hong Li.

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Li, H., Sun, H. & Zhu, W. Solitary Waves and Periodic Waves in a Perturbed KdV Equation. Qual. Theory Dyn. Syst. 19, 83 (2020). https://doi.org/10.1007/s12346-020-00418-w

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