Applications of Differentiable Manifolds and Lie Groups to Partial Differential Equations

Abstract

n this thesis, we study the applications of differentiable manifolds and Lie groups to partial differential Equations (PDEs) which represent some of the important physical phenomena. Our primary objective in this thesis is to identify the differentiable manifolds and its applications to PDEs by symmetries of lie groups, in order to obtain solutions of PDE, especially, minimal surface equation, and a further point is also to discuss the nonclassical method of symmetries to differential equations.