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J. Weiss, “The Panlevé Property for Partial Differential Equations. II: B?cklund Transformation, Lax Pairs, and the Schwarzian Derivative,” Journal of Mathematical Physics, Vol. 24, No. 6, 1983, pp. 1405-1413. Hdoi:10.1063/1.525875

has been cited by the following article:

• TITLE: Solitary Wave Solution of the Two-Dimensional Regularized Long-Wave and Davey-Stewartson Equations in Fluids and Plasmas

  AUTHORS: Omar H. El-Kalaawy, Rafat S. Ibrahim

  KEYWORDS: Exact Solitary Solutions; Extended Mapping Method; Two Dimension Regularized Long Wave and Da Vey-Stewartson Equations; Jacobi Elliptic Functions

  JOURNAL NAME: Applied Mathematics, Vol.3 No.8, August 1, 2012

  ABSTRACT: This paper investigates the solitary wave solutions of the (2+1)-dimensional regularized long-wave (2DRLG) equation which is arising in the investigation of the Rossby waves in rotating flows and the drift waves in plasmas and (2+1) dimensional Davey-Stewartson (DS) equation which is governing the dynamics of weakly nonlinear modulation of a lattice wave packet in a multidimensional lattice. By using extended mapping method technique, we have shown that the 2DRLG-2DDS equations can be reduced to the elliptic-like equation. Then, the extended mapping method is used to obtain a series of solutions including the single and the combined non degenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear partial differential equations (NLPDEs).