Zero-curvature representation for a chiral-type three-field system

D.K. Demskoi, A.G. Meshkov

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8 Citations (Scopus)


The matrix 4×4 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 languageEnglish
Pages (from-to)563-571
Number of pages9
JournalInverse Problems
Issue number3
Publication statusPublished - 2003


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