Approximate and Renormgroup Symmetries

1. Auflage 2009
ISBN: 978-3-642-00228-1
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 147 Seiten

'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 problems in physical science and engineering. Dr. N.H. Ibragimov is a professor at the Department of Mathematics and Science, Research Centre ALGA, Sweden. He is widely regarded as one of the world's foremost experts in the field of symmetry analysis of differential equations; Dr. V. F. Kovalev is a leading scientist at the Institute for Mathematical Modeling, Russian Academy of Science, Moscow.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Preface;6
2;Contents;7
3;Chapter 1 Lie Group Analysis in Outline;10
3.1;1.1 Continuous point transformation groups;10
3.2;1.2 Symmetries of ordinary differential equations;17
3.3;1.3 Integration of first-order equations;25
3.4;1.4 Integration of second-order equations;29
3.5;1.5 Symmetries of partial differential equations;33
3.6;1.6 Three definitions of symmetry groups;40
3.7;1.7 Lie-Backlund transformation groups;45
4;Chapter 2 Approximate Transformation Groups and Symmetries;54
4.1;2.1 Approximate transformation groups;54
4.2;2.2 Approximate symmetries;63
4.3;References;81
5;Chapter 3 Symmetries of Integro- Differential Equations;82
5.1;3.1 Definition and infinitesimal;82
5.2;3.2 Calculation of symmetries illustrated by Vlasov-Maxwell equations;86
5.3;References;103
6;Chapter 4 Renormgroup Symmetries;104
6.1;4.1 Introduction;104
6.2;4.2 Renormgroup algorithm;108
6.3;4.3 Examples;111
6.4;References;120
7;Chapter 5 Applications of Renormgroup Symmetries;121
7.1;5.1 Nonlinear optics;121
7.2;5.2 Plasma physics;137
7.3;References;149
8;Index;150