Novel multiple soliton solutions for some nonlinear PDEs via multiple method


Nisar K. S. , İLHAN O. A. , Abdulazeez S. T. , Manafian J., Mohammed S. A. , Osman M. S.

RESULTS IN PHYSICS, vol.21, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21
  • Publication Date: 2021
  • Doi Number: 10.1016/j.rinp.2020.103769
  • Title of Journal : RESULTS IN PHYSICS
  • Keywords: Multiple Exp-function method, Multiple soliton solutions, Generalized shallow water-like equation, Boiti-Leon-Manna-Pempinelli equation, Generalized variable-coefficient B-type, Kadomtsev-Petviashvili equation, Caudrey-Dodd-Gibbon-Kotera-Sawada equation

Abstract

In this work, the analytic solutions for different types of nonlinear partial differential equations are obtained using the multiple Exp-function method. We consider the stated method for the (3+1)-dimensional generalized shallow water-like (SWL) equation, the (3+1)-dimensional Boiti-Leon- Manna-Pempinelli (BLMP) equation, (3+1)-dimensional generalized variable-coefficient B-type Kadomtsev-Petviashvili (VC B-type KP) equation and the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation. We obtain multi classes of solutions containing one-soliton, two-soliton, and triple-soliton solutions. All the computations have been performed using the software package Maple. The obtained solutions include three classes of soliton wave solutions in terms of one-wave, two-waves, and three-waves solutions. Then the multiple soliton solutions are presented with more arbitrary autocephalous parameters, in which the one, two, and triple solutions localized in all directions in space. Moreover, the obtained solutions and the exact solutions are shown graphically, highlighting the effects of non-linearity. The different types of obtained solutions of aforementioned nonlinear equations arising in fluid dynamics and nonlinear phenomena.