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).
Highlights
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)
In the recent years, seeking exact solutions of nonlinear partial differential equations (NLPDEs) is of great significance, since the nonlinear complex physical phenomena related to the NLPDEs are involved in many fields from physics, fluid mechanics, biology, chemistry kinetics, geochemistry and engineering
The solitary wave solutions of the two dimensional regularized long-wave equation in plasma and rotating flows simulated by using extended mapping method, and we hope these solitary waves are helpful to understand the nonlinear phenomena described by the resonant Davey-Stewartson equation in the fields like capillarity fluids
Summary
In the recent years, seeking exact solutions of nonlinear partial differential equations (NLPDEs) is of great significance, since the nonlinear complex physical phenomena related to the NLPDEs are involved in many fields from physics (plasma physics, optical fibers, solid state physics, nonlinear optics and so on), fluid mechanics, biology, chemistry kinetics, geochemistry and engineering. As mathematical models of the phenomena, the investigation of exact solutions of NLPDEs will help one to understand the mechanism that governs these physical models or to better provide knowledge of the physical problem and possible applications. To this aim, a vast variety of powerful and direct methods for finding the exact significant solutions of the NLPDEs through it is rather difficult have been derived. The Frobenius integrable decompositions (FIDs) and rational function transformations (RFTs) are used to construct exact solutions to NLPDEs with BTs and auto BTs [35,36,37,38,39,40].
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