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arXiv · 2406.17690

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

José M. Escorcia·Erwin Suazo
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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.

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José M. Escorcia, Erwin Suazo. 2024-06-25. On Explicit Solutions for Coupled Reaction-Diffusion and Burgers-Type Equations with Variable Coefficients Through a Riccati System. https://arxiv.org/abs/2406.17690

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