INVARIANT SOLUTION OF SOME DIFFERENTIAL EQUATION

Abstract

In this thesis a recent method viz " Similarity method " described by Sophus Lie, is used to find the solutions of some differential equations frequently appear in describing natural phenomena This method has the following advantages:-

Firstly : Reducing the number of independent variables in differential equation by one .

Secondly: Finding the number of different solutions for the differential equation .

Thirdly : Knowning a previous solution for differential equation, one can construct another one. The thesis consists of an introduction and four charpters

Their contents are as follows :

Chapter I:

In this chapter the author discussed the method under consideration and its use in finding the solutions of partial differential equations as well as producing the I:,rroups of transfonnation.

Chapter II :

The author used the similarity method to find different solutions in five cases for the one - dimensional Fokker Planck's equation.