Author(s)

Yixinni Liu¹, Hongyan Pan^2*

¹Hefei No.1 High School, Hefei, China.
²Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, China.

In this paper, our objective is to explore novel solitary wave solutions of the Burgers-Fisher equation, which characterizes the interplay between diffusion and reaction phenomena. Understanding this equation is crucial for addressing challenges in fluid, chemical kinetics and population dynamics. We tackle this task by employing the Riccati equation and employing various function transformations to solve the Burgers-Fisher equation. By adopting different coefficients in the Riccati equation, we obtain a wide range of exact solutions, many of which have not been previously documented. These abundant solitary wave solutions serve as valuable tools for comprehending the Burgers-Fisher equation and contribute to expanding our knowledge in this field.

Solitary Wave, Soliton, Burger-Fisher Equation, Riccati Equation, Nonlinear Evolution Equation

Liu, Y. and Pan, H. (2023) An Extended Riccati Equation Method to Find New Solitary Wave Solutions of the Burgers-Fisher Equation. Open Journal of Applied Sciences, 13, 1418-1432. doi: 10.4236/ojapps.2023.138112.