Symmetries and Exact Solutions of Nonlinear Dirac Equations

Abstract

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.

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

References in corpus (2)

• Conditional Lie-Bäcklund symmetry and reduction of evolution equations.
• Symmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations

Cited by in corpus (10)

• The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries
• A precise definition of reduction of partial differential equations
• Group classification of heat conductivity equations with a nonlinear source
• Ring Dirac Solitons in Nonlinear Topological Lattices
• Nonlinear Dirac Equations
• Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants
• The Characteristic Functions and Their Typical Values for the Nonlinear Spinors
• Information and Particle Physics
• Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation
• Eigen Equation of the Nonlinear Spinor