Symmetry, Conserved Charges, and Lax Representations of Nonlinear Field Equations: A Unified Approach

Abstract

A certain non-Noetherian connection between symmetry and integrability properties of nonlinear field equations in conservation-law form is studied. It is shown that the symmetry condition alone may lead, in a rather straightforward way, to the construction of a Lax pair, a doubly infinite set of (generally nonlocal) conservation laws, and a recursion operator for symmetries. Applications include the chiral field equation and the self-dual Yang-Mills equation.

15 pages

References in corpus (1)

• Symmetry and Integrability of Classical Field Equations

Cited by in corpus (5)

• A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems
• Recursion Operators for Multidimensional Integrable PDEs
• Bäcklund Transformations: Some Old and New Perspectives
• Symmetry operators and generation of symmetry transformations of partial differential equations
• The Maxwell equations as a Bäcklund transformation