ON EXPLICIT SOLUTIONS FOR COUPLED REACTION-DIFFUSION AND BURGERS-TYPE EQUATIONS WITH VARIABLE COEFFICIENTS THROUGH A RICCATI SYSTEM

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.