Degeneracy of the Characteristic Variety

2014/10/25 by Abraham D. Smith, Smith, Abraham D.
Computer Science · Mathematics · Physics and Astronomy · #35A27 #58A15 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1410.6947

openalex publication_date 2014/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The characteristic variety plays an important role in the analysis of the solution space of partial differential equations and exterior differential systems. This article studies the linear span of this variety, measuring its dimension via an integrable extension of the original system. In the PDE case with locally constant characteristic variety, this extension yields a recursive version of Guillemin normal form, inducing a sequence of foliations on integral manifolds.

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