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New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

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  • Shoukry Ibrahim Atia El-Ganaini

Abstract

The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel′d‐Sokolov‐Wilson system (DSWE), (2 + 1)‐dimensional Davey‐Stewartson system, and generalized Hirota‐Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.

Suggested Citation

  • Shoukry Ibrahim Atia El-Ganaini, 2013. "New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:693076
    DOI: 10.1155/2013/693076
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    References listed on IDEAS

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    1. Feng, Zhaosheng, 2008. "Traveling wave behavior for a generalized fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 481-488.
    2. El-Wakil, S.A. & Abdou, M.A., 2007. "New exact travelling wave solutions using modified extended tanh-function method," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 840-852.
    3. He, Ji-Huan & Abdou, M.A., 2007. "New periodic solutions for nonlinear evolution equations using Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1421-1429.
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