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The integral bifurcation method combined with factoring technique for investigating exact solutions and their dynamical properties of a generalized Gardner equation

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Abstract

It is well known that it is difficult to obtain exact solutions of some partial differential equations with highly nonlinear terms or high order terms because these kinds of equations are not integrable in usual conditions. In this paper, by using the integral bifurcation method and factoring technique, we studied a generalized Gardner equation which contains both highly nonlinear terms and high order terms, some exact traveling wave solutions such as non-smooth peakon solutions, smooth periodic solutions and hyperbolic function solutions to the considered equation are obtained. Moreover, we demonstrate the profiles of these exact traveling wave solutions and discuss their dynamic properties through numerical simulations.

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Acknowledgments

This study was supported the Natural Science Foundation of China under Grant No. 11361023, the Natural Science Foundation of Chongqing Normal University under Grant No. 13XLR20 and the Program Foundation of Chongqing Innovation Team Project in University under Grant No. KJTD201308.

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  1. Department of Mathematics, Chongqing Normal University, Chongqing , 401331, People’s Republic of China

    Weiguo Rui

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  1. Weiguo Rui
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Correspondence to Weiguo Rui.

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Rui, W. The integral bifurcation method combined with factoring technique for investigating exact solutions and their dynamical properties of a generalized Gardner equation. Nonlinear Dyn 76, 1529–1542 (2014). https://doi.org/10.1007/s11071-013-1226-8

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