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Solitary waves solutions of singularly perturbed higher-order KdV equation via geometric singular perturbation method

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Abstract

In this paper, we are concerned with a singularly perturbed higher-order KdV equation, which is considered as a paradigm in nonlinear science and has many applications in weakly nonlinear and weakly dispersive physical systems. Based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of the solitary wave solution for the singularly perturbed KdV equation is investigated by using the geometric singular perturbation theory and dynamical systems approach when the perturbation parameter is suitably small.

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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.

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Authors and Affiliations

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

    Kaige Zhuang, Zengji Du & Xiaojie Lin

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  1. Kaige Zhuang
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  2. Zengji Du
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  3. Xiaojie Lin
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Correspondence to Zengji Du.

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Zhuang, K., Du, Z. & Lin, X. Solitary waves solutions of singularly perturbed higher-order KdV equation via geometric singular perturbation method. Nonlinear Dyn 80, 629–635 (2015). https://doi.org/10.1007/s11071-015-1894-7

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  • DOI: https://doi.org/10.1007/s11071-015-1894-7

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