(G'/G)-Expansion Method to Seek Traveling Wave Solutions for Some Fractional Nonlinear Pdes Arising in Natural Sciences

Abstract

The (G'/G)-expansion method with the aid of symbolic computational system can be used to obtain the traveling wave solutions (hyperbolic, trigonometric and rational solutions) for nonlinear time-fractional evolution equations arising in mathematical physics and biology. In this work, we will process the analytical solutions of the time-fractional classical Boussinesq equation, the time-fractional Murray equation, and the space-time fractional Phi-four equation. With the fact that the method which we will propose in this paper is also a standard, direct and computerized method, the exact solutions for these equations are obtained.

Constructions of the soliton solutions to coupled nonlinear Schrödinger equation with advanced mathematical techniques

“…Nonetheless, nonlinear PDEs, because of their complexity, frequently require simpler analytical solutions. Traveling wave methods involve employing specific strategies to identify exact solutions for particular PDEs by focusing on solutions that display distinct traveling wave characteristics, such as the Kudryashov approach, 3,4 the improved Q-expansion strategy, 5 the ( G ′ G )-expansion method, 6 the ( G ′ G ′ + G+ A )-expansion technique, 7 and more. These techniques help convert a given partial differential equation (PDE) into a more straightforward ordinary differential equation (ODE) that can be easily solved.…”

A Study of Traveling Wave Structures and Numerical Investigations into the Coupled Nonlinear Schrödinger Equation Using Advanced Mathematical Techniques

“…Therefore, developing fundamental and systematic methods for deriving analytical solutions to PDEs has become a popular and fascinating subject for most scholars. Among these techniques, we propose the Kudryashov approach [1,2], the improved Q-expansion strategy [3,4], the G G -expansion method [5], and the Jacobi elliptic expansion [6,7]. These methods are handy for transforming a given PDE into a more straightforward ordinary differential equation (ODE) that can be more easily solved.…”