The Riccati System and a Diffusion-Type Equation
Erwin Suazo, Sergei K. Suslov, Jose M. Vega-Guzman
TL;DR
This paper presents a method to solve diffusion-type equations using Riccati and Ermakov systems, including applications to nonautonomous Burgers-type equations, offering a new approach to these nonlinear PDEs.
Contribution
It introduces a novel solution construction method for diffusion equations via Riccati and Ermakov systems, extending to Burgers-type equations.
Findings
Solution construction method for diffusion equations
Application to nonautonomous Burgers-type equations
Connection between Riccati systems and PDE solutions
Abstract
We discuss a method of constructing solution of the initial value problem for duffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered.
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Taxonomy
TopicsNonlinear Waves and Solitons · Differential Equations and Boundary Problems · Differential Equations and Numerical Methods