On Explicit Solutions for Coupled Reaction-Diffusion and Burgers-Type Equations with Variable Coefficients Through a Riccati System

Authors

Jose M. Escorcia
Erwin Suazo, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2024

Abstract

This work is concerned with the study of explicit solutions for generalized coupled reaction-diffusion and Burgers-type systems with variable coefficients. Including nonlinear models with variable coefficients such as diffusive Lotka-Volterra model, the Gray-Scott model, the Burgers equations. The equations' integrability (via the explicit formulation of the solutions) is accomplished by using similarity transformations and requiring that the coefficients fulfill a Riccati system. We present traveling wave type solutions, as well as solutions with more complex dynamics and relevant features such as bending. A Mathematica file has been prepared as supplementary material, verifying the Riccati systems used in the construction of the solutions.

Recommended Citation

Escorcia, José M., and Erwin Suazo. "On Explicit Solutions for Coupled Reaction-Diffusion and Burgers-Type Equations with Variable Coefficients Through a Riccati System." arXiv preprint arXiv:2406.17690 (2024).