Geodesic
Lax representations for triplets of two-dimensional scalar fields of the chiral type
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 189-205

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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.
Keywords: zero-curvature representations, higher symmetries, conservation laws. 
@article{TMF_2006_148_2_a2,
     author = {D. K. Demskoi and V. G. Marikhin and A. G. Meshkov},
     title = {Lax representations for triplets of two-dimensional scalar fields of the chiral type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {189--205},
     publisher = {mathdoc},
     volume = {148},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a2/}
}
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D. K. Demskoi; V. G. Marikhin; A. G. Meshkov. Lax representations for triplets of two-dimensional scalar fields of the chiral type. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 189-205. http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a2/