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TitleCompletion of Linear Differential Systems to Involution
Author(s) Vladimir P. Gerdt
TypeArticle in Journal
AbstractIn this paper we generalize the involutive methods and algorithms de­vised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic differential field. Given a ranking of derivative terms and an involutive division, we formulate the involutivity conditions which form a basis of involutive algorithms. We present an algorithm for computation of a minimal involutive differential basis. Its correctness and termination hold for any constructive and noetherian involutive division. As two important applications we consider posing of an initial value problem for a linear differential system providing uniqueness of its solution and the Lie symmetry analysis of nonlinear differential equations. In particular, this allows to determine the structure of arbitrariness in general solution of linear systems and thereby to find the size of symmetry group.
Keywordsinvolutive methods and algorithms, involutive division, minimal involutive differential basis
URL http://invo.jinr.ru/papers.phtml
Translation No
Refereed No
Institution JINR (Joint Institute for Nuclear Research)