We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (
Nonlinear evolution equations (NLEEs) describe many problems of solid state physics, nonlinear optics, plasma physics, fluid mechanics, population dynamics and many others which arise in mathematical biology, engineering sciences and other technical arena. In recent years, several methods have been developed to obtain traveling wave solutions for many NLEEs, such as the theta function method [
Recently, Wang et al. [
More recently, Zhang et al. [
Many researchers studied the nonlinear reaction diffusion equation to obtain traveling wave solutions by using different methods. For instance, Zayed and Gepreel [
In this paper, we apply the improved
Suppose the general nonlinear partial differential equation:
The main steps of the improved
Consider the traveling wave variable:
Suppose that the traveling wave solution of (
To determine the integer
Substitute (
Solve the system of algebraic equations with the aid of commercial software Maple and we obtain values for
In this section, we investigate the nonlinear reaction diffusion equation by applying the improved
In this work, we consider the nonlinear reaction diffusion equation involving parameters followed by Zayed and Gepreel [
Using the traveling wave transformation Equation (
Taking the homogeneous balance between
Substituting (
Solving the system of obtained algebraic equations with the aid of algebraic software Maple, we obtain the following.
One has
One has
Substituting the general solution Equation (
When
For example:
if if if
When
For example,
if if if
Substituting (
Again, substituting (
Substituting (
Also, substituting (
It is noteworthy to mention that some of our obtained solutions are in good agreement with the existing results which are shown in Table
Zayed and Gepreel [ | Our solutions |
---|---|
(i) If | (i) If |
(ii) If | (ii) If |
(iii) If | (iii) If |
(iv) If | (iv) If |
Periodic solution for
Periodic solution for
Periodic solution for
Solitons solution for
Periodic solution for
Periodic solution for
Solitons solution for
Solitons solution for
Periodic solution for
Solitons solution for
Solitons solution for
Beyond Table
The graphical illustrations of the solutions are described in the Figures with the aid of Maple.
In this paper, we obtain abundant new exact traveling wave solutions for the nonlinear reaction diffusion equation involving parameters by applying the improved
This paper is supported by the USM short-term grant (reference no. 304/PMATHS/6310072) and the authors would like to express their thanks to the School of Mathematical Sciences, USM, for providing related research facilities. The authors are also grateful to the referee(s) for their valuable comments and suggestions.