Differential-algebraic solutions of the heat equation

2014/05/05 by Victor M. Buchstaber, Buchstaber, Victor M., Elena Yu. Netay +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP

paper · pdf · doi:10.48550/arxiv.1405.0926

11 pages, 6 figures

arxiv created 2014/05/05 · arxiv updated 2014/05/06

Abstract

In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz for such solutions is called the n-ansatz, where n+1 is the order of the differential equation.

Related

• Ordinary differential equations associated with the heat equation
• Hermite, Higher order Hermite, Laguerre type polynomials and Burgers like equations
• Heat Polynomials, Umbral Correspondence and Burgers Equations
• Construction of particular solutions to nonlinear equations of Mathematical Physics by using matrix algebraic equation
• A Recurrence Formula of Solutions for Burgers Equations