Symmetries and Exact Solutions of Nonlinear Dirac Equations

Details Symmetries and Exact Solutions of Nonlinear Dirac Equations Symmetries and Exact Solutions of Nonlinear Dirac Equations

2006-09-18

arxiv.org/abs/math-ph/0609052v1

Mathematical Ukraina Publisher, Kyiv, 1997, 384 pp, ISSN 966-02-0144-3

Physics

Mathematical Physics

electronic version of the book published in 1997 by Institute of Mathematics, Kiev, Ukraine

Scientific paper

The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical solutions of the nonlinear Dirac, Yang-Mills, Maxwell-Dirac, Dirac-d'Alembert, d'Alembert-Hamilton equations; expound a new symmetry approach to variable separation in linear and nonlinear PDEs, which allows, in particular, to classify separable Schroedinger equations. The book offers a uniform and relatively simple presentation of a considerable amount of material that is otherwise not easily available. The basic part of the book contains original results obtained by the authors. It is sure to be of interest to mathematical and theoretical physicists, particularly those working on classical and quantum field theories and on nonlinear dynamical systems.

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