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.
Lie Group Analysis of Nonlinear Partial Differential Equations
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Description
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.
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley...
This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and...
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction...
This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial...
Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the...
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