Formal Solutions of a Class of Pfaffian Systems in Two Variables
Abstract
In this paper, we present an algorithm which computes a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in two variables, based on (Barkatou, 1997). A first step was set in (Barkatou-LeRoux, 2006) where the problem of rank reduction was tackled via the approach of (Levelt, 1991). We give instead a Moser-based approach. And, as a complementary step, we associate to our problem a system of ordinary linear singular differential equations from which the formal invariants can be efficiently derived via the package ISOLDE, implemented in the computer algebra system Maple.
Keywords
Cite
@article{arxiv.1401.5439,
title = {Formal Solutions of a Class of Pfaffian Systems in Two Variables},
author = {Moulay Barkatou and Suzy S. Maddah and Hassan Abbas},
journal= {arXiv preprint arXiv:1401.5439},
year = {2014}
}
Comments
Keywords: Linear systems of partial differential equations, Pfaffian systems, Formal solutions, Moser-based reduction, Hukuhara- Turritin normal form