Equations and Integrals of Motion in Discrete Integrable $A_{k-1}$ Algebra Models

A. P. Protogenov; V. A. Verbus

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Equations and Integrals of Motion in Discrete Integrable $A_{k-1}$ Algebra Models

A. P. Protogenov·V. A. Verbus

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Abstract

We study integrals of motion for Hirota bilinear difference equation that is satisfied by the eigenvalues of the transfer-matrix. The combinations of the eigenvalues of the transfer-matrix are found, which are integrals of motion for integrable discrete models for the $A_{k-1}$ algebra with zero and quasiperiodic boundary conditions. Discrete analogues of the equations of motion for the Bullough-Dodd model and non-Abelian generalization of Liouville model are obtained.

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BibTeX RIS

A. P. Protogenov, V. A. Verbus. 1999-11-19. Equations and Integrals of Motion in Discrete Integrable $A_{k-1}$ Algebra Models. https://arxiv.org/abs/solv-int/9911009

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