The Riccati Differential Equation and a Diffusion-Type Equation

2008/07/28 by Erwin Suazo, Suazo, Erwin, Sergeĭ K. Suslov +3 · 2 citations
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.0807.4349

openalex publication_date 2008/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary functions and certain integrals involving a characteristic function, which should be found as an analytic or numerical solution of the second order linear differential equation with time-dependent coefficients. Some special and limiting cases are outlined. Solution of the corresponding non-homogeneous equation is also found.

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• Mixed superposition rules for Lie systems and compatible geometric structures
• On Schroedinger Equation with Time-Dependent Quadratic Hamiltonian in R^d

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