Geodesic
Laplace Invariants of Two-Dimensional Open Toda Lattices
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 401-421

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We show that Toda lattices with the Cartan matrices $\mathrm{A}_{n}$, $\mathrm{B}_{n}$, $\mathrm{C}_{n}$ и $\mathrm{D}_{n}$ are Liouville-type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants. We show how they can be used to construct conservation laws ($x$ and $y$ integrals) and higher symmetries.
Keywords: symmetries, integrals, generalized invariants.
Mots-clés : Laplace invariants 
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     author = {A. M. Gurieva and A. V. Zhiber},
     title = {Laplace {Invariants} of {Two-Dimensional} {Open} {Toda} {Lattices}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {401--421},
     publisher = {mathdoc},
     volume = {138},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a4/}
}
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A. M. Gurieva; A. V. Zhiber. Laplace Invariants of Two-Dimensional Open Toda Lattices. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 401-421. http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a4/