2024/06/25 by José M. Escorcia, Escorcia, José M., Erwin Suazo +1
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2406.17690
openalex publication_date 2024/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.