Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics: 246 (Mathematics and Its Applications) - Tapa blanda

Fushchich, W.I.; Shtelen, W.M.; Serov, N.I.

 
9789048142446: Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics: 246 (Mathematics and Its Applications)
Tapa blanda
ISBN 10: 904814244X ISBN 13: 9789048142446
Editorial: Springer, 2010

Sinopsis

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.

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Reseña del editor

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.

Reseña del editor

This volume presents an account of the current state of algebraic-theoretic methods as applied to linear and nonlinear multidimensional equations of mathematical and theoretical physics. Equations are considered that are invariant under Euclid, Galilei, Schrödinger, Poincaré, conformal, and some other Lie groups, with special emphasis being given to the construction of wide classes of exact solutions of concrete nonlinear partial differential equations, such as d'Alembert, Liouville, Monge-Ampère, Hamilton-Jacobi, eikonal, Schrödinger, Navier-Stokes, gas dynamics, Dirac, Maxwell-Dirac, Yang-Mills, etc. Ansätze 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 nonlocal transformations is described. Furthermore, the concept of conditional symmetry is introduced and is used to obtain new non-Lie Ansätze for nonlinear 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 will be of interest to researchers, and graduate students in physics and mathematics interested in algebraic-theoretic methods in mathematical and theoretical physics.

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Editorial
Springer
Año de publicación
2010
Idioma
Inglés
ISBN 10 
904814244X
ISBN 13 
9789048142446
Encuadernación
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Número de páginas
464
Contacto del fabricante
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Otras ediciones populares con el mismo título

9780792321460: Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics: 246 (Mathematics and Its Applications)

Edición Destacada

ISBN 10:  0792321464 ISBN 13:  9780792321460
Editorial: Springer, 1993
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