Author(s)

Omar H. El-Kalaawy, Rafat S. Ibrahim

Department of Mathematics, Faculty of Science, Beni-Suef University Beni-Suef 62511, Egypt.

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).

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

El-Kalaawy, O. and Ibrahim, R. (2012) Solitary Wave Solution of the Two-Dimensional Regularized Long-Wave and Davey-Stewartson Equations in Fluids and Plasmas. Applied Mathematics, 3, 833-843. doi: 10.4236/am.2012.38124.