The explicit and traveling wave solutions of the nonlinear Phi-4 model and its implementations

Abstract

Analysis of simple analytical wave solutions to nonlinear evolution equations is a fascinating and growing area of knowledge in highly nonlinear sciences. The Riccati equation rational expansion technique is being used in the paper to establish the exact traveling wave solutions of the Phi-4 model. We have investigated certain types of explicit solutions using this technique, such as periodic, hyperbolic, and rational solutions with some free parameters. The solitary wave solutions are derived from the traveling wave solutions when the parameters are set to particular values. In mathematical physics, it is discovered that the implemented technique is more effective for finding the analytical wave solution of nonlinear evolution models. The approach stands out for its simple and quick computation procedure.