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

Abstract

This paper investigates the solitary wave solutions of the (2+1)-dimensional regularized long-wave (2DRLW) 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 2DRLW-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).

A time-splitting Galerkin finite element method for the Davey–Stewartson equations

“…A. Biswas [13] considered G'/G method and the solitary wave ansatz method to study traveling wave solutions and 1-soliton solution, respectively. O. H. El-Kalaawy and R. S. Ibrahim [16] obtained the solitary wave solutions by using extended mapping method technique. Y. Ohta and J. Yang [20,21] derived the general rogue waves by the bilinear method.…”

Unveiling single soliton solutions for the (3+1)-dimensional negative order KdV–CBS equation in a long wave propagation

“…Soliton theory is used in a variety of scientific fields, including telecommunications, transportation phenomena and many more [4]. NLPDEs are accustomed to simulate a wide range of chemical, biolog-ical, and physical events, and they play an important role in non-linear research [5]. It gives proper evidence and a greater knowledge of physical aspects of the problem, leading to further applications [6][7][8][9].…”

Conservation Laws and Travelling Wave Solutions for a Negative-Order KdV-CBS Equation in 3+1 Dimensions

“…A variety of chemical, biological and physical phenomena are modeled via nonlinear partial differential equations (PDEs) which contribute a key role in nonlinear science [3]. It provides an abundance of physical data and a deeper understanding of the problem's physical characteristics, resulting in additional applications [4][5][6][7].…”