Symmetries of Toda type 3D lattices

2024/09/11 by I. T. Habibullin, Habibullin, I. T., A. R. Khakimova +1
Mathematics · #Advanced Algebra and Geometry #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2409.07017

openalex publication_date 2024/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third order symmetries are presented in explicit form. Corresponding coupled systems are given. An original method for constructing exact solutions to coupled systems is suggested based on the Darboux integrable reductions of the dressing chains. Some new solutions for coupled systems related to the Volterra lattice are presented as illustrative examples.

Related

• Higher symmetries of the lattices in 3D
• On integrable reductions of two-dimensional Toda-type lattices
• Bi-Hamiltonian structures of Toda type systems
• On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries
• New non-Noetherian Symmetries and Multi-Hamiltonian Structures for the Toda Lattice