Symmetry and Integrability of Classical Field Equations

Details Symmetry and Integrability of Classical Field Equations Symmetry and Integrability of Classical Field Equations

2008-03-26

arxiv.org/abs/0803.3688v3

Physics

Mathematical Physics

31 pages, minor corrections on pp.26,28

Scientific paper

A number of characteristics of integrable nonlinear partial differential equations (PDE's) for classical fields are reviewed, such as Backlund transformations, Lax pairs, and infinite sequences of conservation laws. An algebraic approach to the symmetry problem of PDE's is described, suitable for PDE's the solutions of which are non-scalar fields (e.g., are in the form of matrices). A method is proposed which, in certain cases, may "unify" the symmetry and integrability properties of a nonlinear PDE. Application is made to the self-dual Yang-Mills equation and the Ernst equation of General Relativity.

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