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 ValleyFollow

Document Type

Article

Publication Date

3-2025

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 the 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.

Comments

Original published version available at https://doi.org/10.3934/dcdss.2025030

Recommended Citation

Escorcia, José M., and Erwin Suazo. 2025. “On Explicit Solutions for Coupled Reaction-Diffusion and Burgers-Type Equations with Variable Coefficients through a Riccati System.” Discrete and Continuous Dynamical Systems - S, March 17, 0–0. https://doi.org/10.3934/dcdss.2025030.

Publication Title

Discrete and Continuous Dynamical Systems - S

DOI

10.3934/dcdss.2025030