|Title||Gröbner Bases and Involutive Methods for Algebraic and Differential Equations|
|Author(s)|| Vladimir P. Gerdt|
|Type||Article in Journal|
|Abstract||In 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.
|Keywords||involutive methods, partial differential equations, solving nonlinear algebraic and differential equations, involutive bases|
JINR (Joint Institute for Nuclear Research)|