Backlund Transformation for the BC-Type Toda Lattice

Vadim Kuznetsov; Evgeny Sklyanin

doi:10.3842/SIGMA.2007.080

Backlund Transformation for the BC-Type Toda Lattice

Vadim Kuznetsov, Evgeny Sklyanin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study an integrable case of n-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a Backlund transformation and prove its basic properties: canonicity, commutativity and spectrality. The Backlund 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.

Original language	English
Article number	080
Pages (from-to)	1-17
Number of pages	17
Journal	Symmetry integrability and geometry-Methods and applications
Volume	3
DOIs	https://doi.org/10.3842/SIGMA.2007.080
Publication status	Published - 25 Jul 2007

Keywords

Backlund transformation
Toda lattice
integrability
boundary conditions
classical Lie algebras

Access to Document

10.3842/SIGMA.2007.080

Cite this

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abstract = "We study an integrable case of n-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a Backlund transformation and prove its basic properties: canonicity, commutativity and spectrality. The Backlund 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.",

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AB - We study an integrable case of n-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a Backlund transformation and prove its basic properties: canonicity, commutativity and spectrality. The Backlund 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.

KW - Backlund transformation

KW - Toda lattice

KW - integrability

KW - boundary conditions

KW - classical Lie algebras

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