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Dynamics of Travelling Waves to KdV–Burgers–Kuramoto Equation with Marangoni Effect Perturbation

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Abstract

This paper aims to establish the existence of travelling waves for a generalized KdV–Burgers–Kuramoto equation via utilising geometric singular perturbation theory. Firstly, we explore the existence results of orbits for the equation without delay and perturbation by employing Argument Principle. Secondly, the existence of travelling waves for the equation with two types of special delay convolution kernels are proved with the aid of combining the geometric singular perturbation theory, invariant manifold theory and Fredholm orthogonality theorem. Finally, asymptotic behaviors of traveling waves are given with the method of the asymptotic theory.

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Acknowledgements

We express our sincere thanks to the anonymous reviewers for their valuable comments and suggestions for improving the quality of the paper Grant No. 11871251.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, China

    Ke Wang & Zengji Du

  2. School of Mathematics, Southeast University, Nanjing, 211189, Jiangsu, China

    Shuting Chen

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  1. Ke Wang
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  2. Shuting Chen
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  3. Zengji Du
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Correspondence to Zengji Du.

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This work is supported by the Natural Science Foundation of China (Grant No. 12271220) and the Postgraduate Research and Practice Innovation Program of Jiangsu Province (Grant No. KYCX21-2562)

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Wang, K., Chen, S. & Du, Z. Dynamics of Travelling Waves to KdV–Burgers–Kuramoto Equation with Marangoni Effect Perturbation. Qual. Theory Dyn. Syst. 21, 132 (2022). https://doi.org/10.1007/s12346-022-00662-2

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