### Abstract

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 language | English |
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Pages (from-to) | 1034-1048 |

Number of pages | 15 |

Journal | Theoretical and Mathematical Physics |

Volume | 148 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 |

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## Cite this

Demskoi, D. K., Marikhin, V. G., & Meshkov, A. G. (2006). Lax representations for triplets of two-dimensional scalar fields of the chiral-type.

*Theoretical and Mathematical Physics*,*148*(2), 1034-1048. https://doi.org/10.1007/s11232-006-0099-0