### Abstract

The matrix 4Ã—4 zero-curvature representation for a two-dimensional chiral-type system with three fields is constructed. The system under consideration belongs to the class of scalar fields with the Lagrangian L = 1/2 g_{i j} (u)u i_x u j_t + f (u), where g_{ij} is the metric tensor of the three-dimensional reducible Riemann space. This system was found by the authors earlier in the frame of the symmetry method. The zero-curvature representation is computed with the help of the third order symmetry u_t = S(u). This was possible because the hyperbolic system is a nonlocal member in the hierarchy of the evolution systems and the matrix U of the zero-curvature representation is the common one for the whole hierarchy. As the test for non-triviality of the representation the recursion relations for the conserved currents are found.

Original language | English |
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Pages (from-to) | 563-571 |

Number of pages | 9 |

Journal | Inverse Problems |

Volume | 19 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2003 |

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## Cite this

Demskoi, D. K., & Meshkov, A. G. (2003). Zero-curvature representation for a chiral-type three-field system.

*Inverse Problems*,*19*(3), 563-571. https://doi.org/10.1088/0266-5611/19/3/306