Affine Lie algebras, Lax pairs and integrable discrete and continuous systems

2012/05/30 by R. N. Garifullin, Garifullin, Rustem N., I. T. Habibullin +1
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1205.6620

openalex publication_date 2012/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of generalized Toda lattice while semi-discrete systems in the set define the Backlund transform for this Toda lattice and the fully discrete representative of the set can be obtained as a superposition of such kind Backlund transforms. Four linear Zakharov-Shabat type systems taken pairwise realize Lax pairs for these six dynamical systems.

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