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Single-peak solitary wave solutions for the generalized Korteweg–de Vries equation

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Abstract

The qualitative theory of differential equations is applied to the generalized Korteweg–de Vries (KdV) equation. Smooth, peaked and cusped solitary wave solutions of the generalized KdV equation under the boundary condition \(\lim \nolimits _{x \rightarrow \pm \infty }{u}=A \) (\(A\) is a constant) are obtained. The parametric conditions of existence of the smooth, peaked and cusped solitary wave solutions are given using the phase portrait analytical technique. Asymptotic analysis is provided for smooth, peaked and cusped solitary wave solutions of the generalized KdV equation.

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Acknowledgments

Useful suggestions and comments made by the referee are gratefully acknowledged. This research was supported by the National Natural Science Foundation of China (11401274/A010702, 11361017/A010702,  11301455) and Natural Science Foundation of Jiangxi Province (20122BAB201013). Science and technology landing project of colleges and universities in Jiangxi Province (KJLD14092, KJLD13093 )

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Authors and Affiliations

  1. Information Technology Center, Jiujiang University, Jiujiang, 332005, People’s Republic of China

    Lilin Ma

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

    Hong Li & Jun Ma

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  1. Lilin Ma
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  2. Hong Li
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  3. Jun Ma
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Correspondence to Hong Li.

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Ma, L., Li, H. & Ma, J. Single-peak solitary wave solutions for the generalized Korteweg–de Vries equation. Nonlinear Dyn 79, 349–357 (2015). https://doi.org/10.1007/s11071-014-1668-7

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  • DOI: https://doi.org/10.1007/s11071-014-1668-7

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