Geodesic
Symmetries of nonlinear hyperbolic systems of the~Toda chain type
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 2, pp. 344-355

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We consider hyperbolic systems of equations that have full sets of integrals along both characteristics. The best known example of models of this type is given by two-dimensional open Toda chains. For systems that have integrals, we construct a differential operator that takes integrals into symmetries. For systems of the chosen type, this proves the existence of higher symmetries dependent on arbitrary functions.
Mots-clés : Liouville equation
Keywords: Toda chain, integral, higher symmetry, hyperbolic system of partial differential equations, Noether theorem. 
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     author = {V. V. Sokolov and S. Ya. Startsev},
     title = {Symmetries of nonlinear hyperbolic systems of {the~Toda} chain type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {344--355},
     publisher = {mathdoc},
     volume = {155},
     number = {2},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_2_a12/}
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V. V. Sokolov; S. Ya. Startsev. Symmetries of nonlinear hyperbolic systems of the~Toda chain type. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 2, pp. 344-355. http://geodesic.mathdoc.fr/item/TMF_2008_155_2_a12/