Theoretical and Mathematical Physics

, Volume 148, Issue 2, pp 1034–1048 | Cite as

Lax representations for triplets of two-dimensional scalar fields of the chiral type

  • D. K. Demskoi
  • V. G. Marikhin
  • A. G. Meshkov


We consider two-dimensional relativistically invariant systems with a three-dimensional reducible configuration space and a chiral-type Lagrangian that admit higher symmetries given by polynomials in derivatives up to the fifth order. Nine such systems are known: two are Liouville-type systems, and zero-curvature representations for two others have previously been found. We here give zero-curvature representations for the remaining five systems. We show how infinite series of conservation laws can be derived from the established zero-curvature 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.


zero-curvature representations higher symmetries conservation laws 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • D. K. Demskoi
    • 1
  • V. G. Marikhin
    • 2
  • A. G. Meshkov
    • 1
  1. 1.Orel State UniversityOrelRussia
  2. 2.Landau Institute for Theoretical PhysicsRASMoscowRussia

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