The Geometric Structure 0f Group Invariant Solutions Of Difierential Operators

Abstract

Abstract Group invariant solutions have been used to a great effect in the description of the asymptotic behaviour of many general solution to systems of partial differential equations. The rigorous foundation of the general method for constructing group — invariant solution requires advanced formalism of differential geometry. From our point of view the Fibre bundle over a quotient manifold approach seems very promising in analyzing the mechanism of group-invariant solutions and classifying different types of behaviour of a system. In this research we shall explore the bundle over a quotient space approach. Our applications will are on some partial differential equations.