Geodesic
Bäcklund Transformation for the BC-Type Toda Lattice
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study an integrable case of $n$-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a Bäcklund transformationand prove its basic properties: canonicity, commutativity and spectrality. The Bäcklund transformation can be also viewed as a discretized time dynamics. Two Lax matrices are used: of order 2 and of order $2n+2$, which are mutually dual, sharing the same spectral curve.
Keywords: Bäcklund transformation; Toda lattice; integrability; boundary conditions; classical Lie algebras. 
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     title = {B\"acklund {Transformation} for the {BC-Type} {Toda} {Lattice}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a79/}
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Vadim Kuznetsov; Evgeny Sklyanin. Bäcklund Transformation for the BC-Type Toda Lattice. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a79/

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