Solving Some Nonlinear Partial Differential Equations by GERFM

Abstract

We study using the method of generalized Hexponential rational function method (GERFM) to acquire some exact optical solitons for the dimensionless form of some equations such as (1 + 1) generalized Benjamin–Bona–Mahony (GBBM) equation. To this end, by transformation: 𝑢(𝑥,𝑡) = 𝜓(𝜂), 𝜂 = 𝑘𝑥 − 𝜃𝑡. Where k and θ are constant values, the equations are converted into a nonlinear ODE. Second, the nonlinear ODE is solved according to a linear combination of the given basis functions. In this case, an algebraic equation is constructed. The solution of the nonlinear ODE yields the same solution of the original nonlinear PDE. In this paper, we will discuss about exact solutions of Generalized Benjamin-BonaMahony, Wu-Zhang equation and Fisher equation. we present generalized exponential rational function method that is abbreviated by GERFM. We use it to find an exact solution for some equations that we present in the sequel