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Semidiscrete Toda lattices

Abstract

We study integrable cutoff constraints for a semidiscrete Toda lattice. We construct a Lax representation for a semidiscrete analogue of lattices corresponding to simple Lie algebras of the C series. We introduce nonlocal variables in terms of which the symmetries of the infinite semidiscrete lattice can be expressed, and we classify cutoff constraints of a certain form compatible with the symmetries of the infinite lattice.

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Author information

Correspondence to S. V. Smirnov.

Additional information

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 172, No. 3, pp. 387–402, September, 2012.

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Smirnov, S.V. Semidiscrete Toda lattices. Theor Math Phys 172, 1217–1231 (2012). https://doi.org/10.1007/s11232-012-0109-3

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Keywords

  • semidiscrete Toda lattice
  • Lax representation
  • symmetry
  • integrable cutoff constraint