D K Demskoi and A G Meshkov 2003 Inverse Problems 19 563 doi:10.1088/0266-5611/19/3/306
D K Demskoi and A G Meshkov
Show affiliationsThe 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 = 1/2gij (u)uxi u tj + f(u), where gij 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 ut = 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.
Issue 3 (June 2003)
Received 7 November 2002, in final form 17 March 2003
Published 4 April 2003
D K Demskoi and A G Meshkov 2003 Inverse Problems 19 563
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