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    All exact traveling wave solutions of the combined KdV-mKdV equation

    231833_231831.pdf (294.8Kb)
    Access Status
    Open access
    Authors
    Huang, Y.
    Wu, Yong Hong
    Meng, F.
    Yuan, W.
    Date
    2014
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Huang, Y. and Wu, Y.H. and Meng, F. and Yuan, W. 2014. All exact traveling wave solutions of the combined KdV-mKdV equation. Advances in Difference Equations. 2014: Article ID 261.
    Source Title
    Advances in Difference Equations
    DOI
    10.1186/1687-1847-2014-261
    ISSN
    1687-1839
    School
    Department of Mathematics and Statistics
    Remarks

    This open access article is distributed under the Creative Commons license http://creativecommons.org/licenses/by/4.0/

    URI
    http://hdl.handle.net/20.500.11937/7341
    Collection
    • Curtin Research Publications
    Abstract

    In this article, we employ the complex method to obtain all meromorphic solutions of complex combined Korteweg-de Vries-modified Korteweg-de Vries equation (KdV-mKdV equation) at first, then we find all exact traveling wave solutions of the combined KdV-mKdV equation. The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic exact traveling wave solutions of the combined KdV-mKdV equation are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions wr,2(z)wr,2(z) and simply periodic solutions ws,2(z)ws,2(z) such that they are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role in finding exact solutions in mathematical physics. We also give some computer simulations to illustrate our main results.

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