Lax representations for triplets of two-dimensional scalar fields of the chiral type |
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Authors: | D K Demskoi V G Marikhin A G Meshkov |
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Institution: | (1) Orel State University, Orel, Russia;(2) Landau Institute for Theoretical Physics, RAS, Moscow, Russia |
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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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 189–205, August, 2006. |
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Keywords: | zero-curvature representations higher symmetries conservation laws |
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