Ideals of partial differential equations

2016/11/12 by О. В. Капцов, Oleg V. Kaptsov, Kaptsov, Oleg V.
Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation #math-ph #math.DS #math.MP

paper · pdf · doi:10.48550/arxiv.1611.05441

20 pages

arxiv created 2016/11/12 · openalex publication_date 2016/11/12 · arxiv updated 2016/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gröbner bases to clarify crucial notions concerning compatibility such as passivity (involution) and reducibility. One obtains sufficient conditions for a differential system to be passive and prove that such systems generate manifolds in the jet space. Some examples of constructions of passive systems associated with the sinh-Gordon equation are given.

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