Optical Soliton Solutions of Burgers-Fisher and Burgers-Huxley Equations

Abstract

In this study, we investigate the soliton solutions of two prominent nonlinear partial differential equations: the Burgers-Fisher equation and the Burgers-Huxley equation. These models are instrumental in describing a variety of physical, biological, and ecological phenomena where both nonlinear advection and reaction-diffusion mechanisms play significant roles. To derive the soliton solutions of these equations, we employ the Bernoulli sub-ODE method, a powerful analytical technique for solving nonlinear ODEs. This method transforms the original partial differential equations into more tractable forms, facilitating the discovery of soliton solutions. Our findings demonstrate the existence of stable, localized wave solutions for both equations, providing deeper insights into the wave dynamics governed by these models.