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Bifurcations of Traveling Wave Solutions for a Modified Novikov’s Cubic Equation

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Abstract

Exact traveling solutions for a modified Novikov’s cubic equation is considered based on the bifurcation method of dynamical systems in this paper. The two-dimensional system of modified Novikov’s cubic equation exists singular curve \(\phi ^2+a^2y^2=R\) when \(R>0\) and then it is proved that the corresponding traveling wave system of the modified Novikov’s cubic equation exists smooth solitary wave solutions and breaking wave solutions.

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Acknowledgements

The author is grateful to Professor Zhijun Qiao for his enthusiastic guidance and help during her visit to University of Texas-Rio Grande Valley, USA. It is also a pleasure to thank the Professor Shengqiang Tang, Guilin University of Electronic Technology, for several enlightening advice and illuminating discussions. This work were supported by National Natural Science Foundation of China (Nos. 41461110, 11461001) and Guangxi College Enhancing Youths Capacity Project (KY2016LX315), Guangxi University of Finance and Economics project (2017QN09).

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  1. Deparment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, 530003, Guangxi, People’s Republic of China

    Minzhi Wei

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Wei, M. Bifurcations of Traveling Wave Solutions for a Modified Novikov’s Cubic Equation. Qual. Theory Dyn. Syst. 18, 667–686 (2019). https://doi.org/10.1007/s12346-018-0306-z

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