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Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation

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Abstract

By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.

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Acknowledgements

This research is supported by National Natural Science Foundation of China (Nos 11162004, 11461021), Guangxi Natural Science Foundation (No. 2015GXNS FBA139004) and Innovation Project of GUET Graduate Education (No. YJCXS201557).

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, People’s Republic of China

    JUNJUN XIAO, DAHE FENG, XIA MENG & YUANQUAN CHENG

  2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou, 550025, People’s Republic of China

    DAHE FENG

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  1. JUNJUN XIAO
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  2. DAHE FENG
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  4. YUANQUAN CHENG
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Correspondence to JUNJUN XIAO.

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XIAO, J., FENG, D., MENG, X. et al. Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation. Pramana - J Phys 88, 17 (2017). https://doi.org/10.1007/s12043-016-1321-8

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  • DOI: https://doi.org/10.1007/s12043-016-1321-8

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