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Modified method of simplest equation for obtaining exact solutions of the Zakharov–Kuznetsov equation, the modified Zakharov–Kuznetsov equation, and their generalized forms

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Abstract

In this paper, we study the application of a version of the method of simplest equation for obtaining exact traveling wave solutions of the Zakharov–Kuznetsov equation, the modified Zakharov–Kuznetsov equation, and their generalized forms. The Duffing-type equation is used as simplest auxiliary equation. In the meantime, the proposed method is proved to be a powerful mathematical tool for obtaining exact solutions of nonlinear partial differential equations in mathematical physics.

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Acknowledgments

All the authors deeply appreciate all the anonymous reviewers for their helpful and constructive suggestions, which can help improve this paper further. This work is supported by the National Natural Science Foundation of China (Nos. 11101029, 11271362 and 11375030), the Fundamental Research Funds for the Central Universities, Beijing City Board of Education Science and Technology Key Project No. KZ201511232034, Beijing Nova program No. Z131109000413029, and Beijing Finance Funds of Natural Science Program for Excellent Talents No. 2014000026833ZK19.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Science and Technology Beijing, Beijing, 100083, China

    Jianping Yu

  2. School of Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Deng-Shan Wang

  3. Department of Mathematics, Beijing University of Chemical Technology, Beijing, 100029, China

    Yongli Sun & Suping Wu

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  1. Jianping Yu
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  2. Deng-Shan Wang
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  3. Yongli Sun
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Correspondence to Yongli Sun.

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Yu, J., Wang, DS., Sun, Y. et al. Modified method of simplest equation for obtaining exact solutions of the Zakharov–Kuznetsov equation, the modified Zakharov–Kuznetsov equation, and their generalized forms. Nonlinear Dyn 85, 2449–2465 (2016). https://doi.org/10.1007/s11071-016-2837-7

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