Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Abstract

The present study investigates the lump, one-stripe, lump-stripe, and breather wave solutions to the (2+1)-dimensional Sawada-Kotera equation using the Hirota bilinear method. For lump and lump-stripe solutions, a quadratic polynomial function, and a quadratic polynomial function in conjunction with an exponential term are assumed for the unknown function f giving the solution to the mentioned equation, respectively. On the other hand, only an exponential function is considered for one-stripe solutions. Besides, the homoclinic test approach is adopted for constructing breather wave solutions. The propagations of the attained lump, lump-stripe, and breather wave solutions are shown through some graphical illustrations. The graphical outputs demonstrate that the lump wave moves along the straight line and exponentially decreases away from the origin of the spatial domain. On the other hand, lump-kink solutions illustrate the fission and fusion interaction behaviors upon the selection of the free parameters. Fission and fusion processes show that the stripe soliton splits into a stripe soliton and a lump soliton, and then the lump soliton merges into one stripe soliton. In addition, the achieved breather waves illustrate the periodic behaviors in the xy -plane. The outcomes of the study can be useful for a better understanding of the physical nature of long waves in shallow water under gravity.

Employing the exp $(-\varphi(z))$ - Expansion Method to Find Analytical Solutions for a (2+1)-dimensional Combined KdV-mKdV Equation

“…Because many nonlinear phenomena existing in nature and various fields can be described as NLPDEs. More importantly, the solutions of NLPDEs can account for these complex phenomena as well as applying in these fields [1]- [12], such as atmosphere, optical fiber communications and fluid mechanics. There is a series of NLPDEs, for example, the KdV equation, the KP equation and the Schrödinger equation.…”