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TitleGröbner Bases and Involutive Methods for Algebraic and Differential Equations
Author(s) Vladimir P. Gerdt
TypeArticle in Journal
AbstractIn this paper we consider and illustrate by examples some recently developed com­puter algebra methods for analysis and for solving nonlinear algebraic and differen­tial equations. The foundation of those methods is either transformation of initial equations to an equivalent, often called standard, form or their reduction to a finite set of standard form subsystems. As a standard form we consider here one or an­ other Groebner basis with special emphasis on its involutive extension. Applications to symmetry and integrability analysis of partial differential equations and solving
polynomial equation systems are singled out as possible applications.
Keywordsinvolutive methods, partial differential equations, solving nonlinear algebraic and differen­tial equations, involutive bases
URL http://invo.jinr.ru/papers.phtml
Translation No
Refereed No
Institution JINR (Joint Institute for Nuclear Research)