Introduction

Partial differential equations, also called evolution equations, are fundamental in many physical, chemical, biological, and ecological problems to represent, for instance, the motion of the isolated waves, localized in a small part of space in many fields such as optical fibers, neural physics, solid state physics, hydrodynamics, diffusion process, plasma physics and nonlinear optics (heat equation, Klein-Gordon equation, Euler-Lagrange equation, Burgers equation, Korteweg-de Vries equation, Boussinesq equation, etc.).