On factorization and solution of multidimensional linear partial differential equations

2006/09/13 by S. P. Tsarëv, Tsarev, S. P.
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Exactly Solvable and Integrable Systems (nlin.SI) #F.2.2 #FOS: Computer and information sciences #FOS: Physical sciences #Numerical methods for differential equations #Polynomial and algebraic computation #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.cs/0609075

openalex publication_date 2006/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a method of obtaining closed-form complete solutions of certain second-order linear partial differential equations with more than two independent variables. This method generalizes the classical method of Laplace transformations of second-order hyperbolic equations in the plane and is based on an idea given by Ulisse Dini in 1902.

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