Two effective methods for extract soliton solutions of the reaction-diffusion equations

In this present study, we reduce the fractional reaction–diffusion equation to a traditional differential equation using the fractional complex transformation and consider the Landau Lifshitz (LLG) equation. Moreover, by using the generalized exponential rational function method and Kudryashov's method respectively we extract new exact and solitary wave solutions for these equations. Some plots of some presented new solutions are represented to exhibit wave characteristics. All results in this paper are essential to understand the physical meaning and behavior of the investigated equation that sheds light on the importance of investigating various nonlinear wave phenomena in mathematical physics.

Keywords:

fractional reaction–diffusion equation Landau Lifshitz(LLG) , Kudryashov's method , solitary wave , rational function method , partial differential equation