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Geometric singular perturbation method to the existence and asymptotic behavior of traveling waves for a generalized Burgers–KdV equation

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Abstract

In this paper, we discuss the existence and asymptotic behavior of traveling waves for a generalized Burgers–KdV equation. We show the heteroclinic orbits of the associated ordinary differential equations for the generalized Burgers–KdV equation with a special convolution kernel and then establish the existence result of traveling wave solutions for the Burgers–KdV equation by employing geometric singular perturbation theory and the linear chain trick. And the asymptotic behavior of traveling waves is obtained by using the standard asymptotic theory.

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Acknowledgments

This work is supported by the Natural Science Foundation of China (Grant No. 11471146), PAPD of Jiangsu Higher Education Institutions and postgraduate training project of Jiangsu Province and Jiangsu Normal University. The authors express their sincere thanks to the anonymous reviewers for their valuable comments and suggestions for improving the quality of the paper.

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

    Ying Xu, Zengji Du & Lei Wei

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  1. Ying Xu
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  2. Zengji Du
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  3. Lei Wei
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Correspondence to Zengji Du.

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Xu, Y., Du, Z. & Wei, L. Geometric singular perturbation method to the existence and asymptotic behavior of traveling waves for a generalized Burgers–KdV equation. Nonlinear Dyn 83, 65–73 (2016). https://doi.org/10.1007/s11071-015-2309-5

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  • DOI: https://doi.org/10.1007/s11071-015-2309-5

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