Solitary wave solution of (2+1)-dimensional Chaffee–Infante equation using the modified Khater method

Abstract

Most of the nonlinear phenomena are described by partial differential equation in natural and applied sciences such as fluid dynamics, plasma physics, solid state physics, optical fibers, acoustics, biology and mathematical finance. The solutions of a wide range of nonlinear evolution equations exhibit the wave behavior corresponding to the underlying physical systems. In particular, solitary wave solutions and soliton solutions are of great interest for researchers owing to many applications in different areas of science. The behavior of gas diffusion in a homogeneous medium is described by the (2+1)-dimensional Chaffee–Infante equation. In the present study, the modified Khater method is used to solve (2+1)-dimensional Chaffee–Infante equation because it provides various forms of solitons. The bright, dark, and periodic traveling wave patterns are produced by choosing different values of parameters. The solutions are presented graphically through 2D, 3D and contour graphs. The obtained solutions are demonstrated that the modified Khater method is a more useful tool than the existing techniques for solving such nonlinear problems.

Keywords

• Chaffee–Infante equation
• Modified Khater method
• Solitary waves
• Solitons