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Separation Transformation and a Class of Exact Solutions to the Higher‐Dimensional Klein‐Gordon‐Zakharov Equation

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  • Jing Chen
  • Ling Liu
  • Li Liu

Abstract

The separation transformation method is extended to the (n + 1)‐dimensional Klein‐Gordon‐Zakharov equation describing the interaction of the Langmuir wave and the ion acoustic wave in plasma. We first reduce the (n + 1)‐dimensional Klein‐Gordon‐Zakharov equation to a set of partial differential equations and two nonlinear ordinary differential equations of the separation variables. Then the general solutions of the set of partial differential equations are given and the two nonlinear ordinary differential equations are solved by extended F‐expansion method. Finally, some new exact solutions of the (n + 1)‐dimensional Klein‐Gordon‐Zakharov equation are proposed explicitly by combining the separation transformation with the exact solutions of the separation variables. It is shown that, for the case of n ≥ 2, there is an arbitrary function in every exact solution, which may reveal more nontrivial nonlinear structures in the high‐dimensional Klein‐Gordon‐Zakharov equation.

Suggested Citation

  • Jing Chen & Ling Liu & Li Liu, 2014. "Separation Transformation and a Class of Exact Solutions to the Higher‐Dimensional Klein‐Gordon‐Zakharov Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:974050
    DOI: 10.1155/2014/974050
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    References listed on IDEAS

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    1. Wang, Dengshan & Zhang, Hong-Qing, 2005. "Further improved F-expansion method and new exact solutions of Konopelchenko–Dubrovsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 601-610.
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