Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics / Edition 1

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

Overview

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.

Product Details

ISBN-13:	9780792321460
Publisher:	Springer Netherlands
Publication date:	02/28/1993
Series:	Mathematics and Its Applications , #246
Edition description:	1993
Pages:	435
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1. Poincare Invariant Nonlinear Scalar Equations.- 2. Poincare-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 3. Some applications of Campbell-Baker-Hausdorff operator calculus.- Appendix 6. Compatibility and solutions of the overdetermined d’Alembert-Hamiltonsystem.- Appendix 8. On nonlocal symmetries of nonlinear heat equation.- References.- Additional References.

Editorial Reviews

An updated, revised, and extended translation of the Russian work published by Nauka (Kiev) in 1989. Equations invariant under Euclid, Galilei, Schrodinger, Poincare, conformal, and some other Lie groups are considered. Among the other topics: formulae for generating solutions via conformal transformations for scalar, spinor, vector, and tensor fields with arbitrary conformal degree; the classical three-body problem; the symmetry of some integro-differential equations; and the concept of conditional symmetry. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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