Lax representations for triplets of twodimensional scalar fields of the chiral type
Abstract
We consider twodimensional relativistically invariant systems with a threedimensional reducible configuration space and a chiraltype Lagrangian that admit higher symmetries given by polynomials in derivatives up to the fifth order. Nine such systems are known: two are Liouvilletype systems, and zerocurvature representations for two others have previously been found. We here give zerocurvature representations for the remaining five systems. We show how infinite series of conservation laws can be derived from the established zerocurvature representations. We give the simplest higher symmetries; others can be constructed from the conserved densities using the Hamiltonian operator. We find scalar formulations of the spectral problems.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 August 2006
 DOI:
 10.1007/s1123200600990
 Bibcode:
 2006TMP...148.1034D
 Keywords:

 zerocurvature representations;
 higher symmetries;
 conservation laws