Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics

W. I. Fushchich

ISBN 10: 0792321464 / ISBN 13: 9780792321460

Editore: Springer, Springer, 1993

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [55-109, 176-189, 13-16, 7\*-14\*,23\*, 24\*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.

Codice articolo 9780792321460

Dati bibliografici

• Titolo: Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics
• Editore: Springer, Springer
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 0792321464
• ISBN 13: 9780792321460
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 30 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 30 millimetri di profondità
• Peso: 863 grammi

Descrizione articolo

Riassunto

This volume presents an account of the current state of algebraic-theoretic methods as applied to linear and non-linear multidimensional equations of mathematical and theoretical physics. Equations are considered that are invariant under Euclid, Galilei, Schroedinger, Poincare, conformal, and some other Lie groups, with special emphasis being given to the construction of wide classes of exact solutions of concrete non-linear partial differential equations, such as d'Alembert, Liouville, Monge-Ampere, Hamilton-Jacobi, eikonal, Schroedinger, Navier-Stokes, gas dynamics, Dirac, Maxwell-Dirac, Yang-Mills, et al. Ansaetze for spinor, as well as scalar and vector fields are described and formulae for generating solutions via conformal transformations are found explicitly for scalar, spinor, vector, and tensor fields with arbitrary conformal degree. The classical three-body problem is considered for the group-theoretic point of view. The symmetry of integro-differential equations is also studied, and the method of finding final non-local transformations is described. Furthermore, the concept of conditional symmetry is introduced and is used to obtain new non-Lie Ansaetze for non-linear heat and acoustic equations. The volume comprises an introduction, which presents a brief account of the main ideas, followed by five chapters, appendices, and a comprehensive bibliography. This book should be of interest to researchers, and graduate students in physics and mathematics interested in algebraic-theoretic methods in mathematical and theoretical physics.

Contenuti

Preface. Preface to the English Edition. Introduction. 1. Poincaré Invariant Nonlinear Scalar Equations. 2. Poincaré-Invariant Systems of Nonlinear PDEs. 3. Euclid and Galilei Groups and Nonlinear PDEs for Scalar Fields. 4. System of PDEs Invariant Under the Galilei Group. 5. Some Special Questions. Appendix 1: Jacobi Elliptic Functions. Appendix 2: P(1,3)-Nonequivalent One-Dimensional Subalgebras of the Extended Poincaré Algebra AP(1,3). Appendix 3: Some Applications of Campbell-Baker-Hausdorff Operator Calculus. Appendix 4: Differential Invariants (DI) of Poincaré Algebras (AP(1,n), AP(1,n) and Conformal Algebra AC(1,n). Appendix 5: Differential Invariants (DI) of Galilei Algebras AG(1,n), AG(1,n) and Schrödinger Algebra ASch(1,n). Appendix 6: Compatibility and Solutions of the Overdetermined d'Alembert-Hamilton-System. Appendix 7: Q-Conditional Symmetry of the Heat Equation. Appendix 8: On Nonlocal Symmetries of Nonlinear Heat Equation. References. Additional References. Index.