Approximate and Renormgroup Symmetries (eBook)

N. Kh. Ibragimov, Vladimir F. Kovalev (Autoren)

eBook Download: PDF

2009 | 2009
III, 147 Seiten
Springer Berlin (Verlag)
978-3-642-00228-1 (ISBN)

Infos

'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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 14.11.2009
• Reihe/Serie: Nonlinear Physical Science
• Reihe/Serie: Nonlinear Physical Science
• Zusatzinfo: III, 147 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• Schlagworte: Approximate symmetries and renormgroup symmetries • Approximate transformation groups • HEP • Lie group analysis • Mathematical Modeling • Nonlinear Optics • NPS • Plasma physics • Symmetries of integro-differential equations
• ISBN-10: 3-642-00228-5 / 3642002285
• ISBN-13: 978-3-642-00228-1 / 9783642002281