Lie Group Analysis of Nonlinear Partial Differential Equations

This book serves a strong and simple introduction to the theory of symmetry analysis. The concept of nonlinear partial differential equations is deeply looked into with the nonlinear system of coupled Korteweg-de Vries equations taken as an example. The reader is introduced to the Lie groups and Lie's criterion for computing Lie point symmetries. We also illustrate how these symmetries can be used to reduce system of partial differential equations and linearise them where possible. This helps to construct special exact solutions.We also introduce the reader to computation of conservation laws by the method of multipliers and some of ther applications of these conservation laws. In addition, the symmetries have been used to compute conservation laws by applying Ibragimov's Conservation Theorem. We have also included the physical interpretation of some of the conservation laws. It is my sincere hope that you enjoy reading the book in the same manner I enjoyed writing it.

Autorentext

Joseph is a master's graduate from the University of Stellenbosch and the African Institute for Mathematical Sciences in South Africa. He has taken up courses in Functional Analysis with Auburn University in USA and Mathematical Analysis with the International Mathematics Master. Joseph looks forward to pursuing his PhD in Analysis in Europe.