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

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

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1034-1048
Number of pages15
JournalTheoretical and Mathematical Physics
Issue number2
Publication statusPublished - 2006


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