Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics

ISBN-13: 9780792321460 / Angielski / Twarda / 1993 / 435 str.

Vil'gel'm Il'ich Fushchich; W. I. Fushchich; W. M. Shtelen

Opis

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."

Spis treści

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.