Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lies striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail.

• This is the first modern text on ordinary differential equations where the...

Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra.
Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Backlund, conditional and...

Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra.
Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Backlund, conditional and...

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R.van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches....

"Approximate and Renormgroup Symmetries" deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations.

The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear...

Contains the traditional methods of ordinary and partial differential equations with Lie group analysis by the author's own theoretical developments. This book presents the mathematical curricula based on symmetry and invariance principles. It develops analytical skills in classical and Lie's methods for solving linear and nonlinear equations.

A monograph dealing with the applications of the Lie group analysis to the modeling equations governing internal wave propagation in the deep ocean. It presents a fresh approach to describe the nonlinear interactions of internal waves in the ocean. It investigates oceanic internal waves through the prism of Lie group analysis.

These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models.

This book is based on extensive experience of teaching mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide a universal and effective method for solving nonlinear differential equations analytically. An introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.