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Traveling Wave Solutions of the Kadomtsev‐Petviashvili‐Benjamin‐Bona‐Mahony Equation

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  • Zhengyong Ouyang

Abstract

We use bifurcation method of dynamical systems to study exact traveling wave solutions of a nonlinear evolution equation. We obtain exact explicit expressions of bell‐shaped solitary wave solutions involving more free parameters, and some existing results are corrected and improved. Also, we get some new exact periodic wave solutions in parameter forms of the Jacobian elliptic function. Further, we find that the bell‐shaped waves are limits of the periodic waves in some sense. The results imply that we can deduce bell‐shaped waves from periodic waves for some nonlinear evolution equations.

Suggested Citation

  • Zhengyong Ouyang, 2014. "Traveling Wave Solutions of the Kadomtsev‐Petviashvili‐Benjamin‐Bona‐Mahony Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:943167
    DOI: 10.1155/2014/943167
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    References listed on IDEAS

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    1. Wazwaz, Abdul-Majid, 2008. "The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1505-1516.
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