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The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions

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  • Shoukry Ibrahim Atia El-Ganaini

Abstract

The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1)‐dimensional hyperbolic nonlinear Schrodinger (HNLS) equation, the generalized nonlinear Schrodinger (GNLS) equation with a source, and the higher‐order nonlinear Schrodinger equation in nonlinear optical fibers. 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.

Suggested Citation

  • Shoukry Ibrahim Atia El-Ganaini, 2013. "The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:349173
    DOI: 10.1155/2013/349173
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    References listed on IDEAS

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    1. Abdou, M.A., 2008. "New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 949-955.
    2. Biao Li, 2007. "A Generalized Sub-Equation Expansion Method And Its Application To The Nonlinear Schrödinger Equation In Inhomogeneous Optical Fiber Media," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1187-1201.
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