Symmetry Analysis

We have learnt the qualitative analysis of nonlinear systems in previous chapters. Symmetry is an inherent property of natural phenomena as well as manmade devices. Naturally, the concept of symmetry is exploited to study the linear as well as nonlinear problems. Keeping in mind the immense importance of symmetry, particularly in analyzing nonlinear systems we devote this chapter on basic idea of group of transformations, Lie group of transformations, Lie group of transformations, some theorems on Lie symmetry, its invariance, Invariance principle and algorithm, and symmetry analysis of some physical systems.