2007/10/29 by P. Santini, Paolo Maria Santini, Adam Doliwa +1 · 7 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Geometry #Homogeneous space #Integrable system #Laplace transform #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Quantum mechanics #Square (algebra) #Square lattice #Square-integrable function #Toda lattice #Type (biology) #nlin.PS #nlin.SI
paper · pdf · doi:10.1103/physreve.77.056601
published in Physical Review E 77(5), 056601 (American Physical Society) · 22 pages, 4 figures
arxiv created 2007/10/29 · openalex publication_date 2008/05/01 · arxiv updated 2010/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. We construct other examples of integrable dynamics of Toda type on the square lattice, as well as on the triangular lattice, as nonlinear symmetries of the discrete Laplace equations on square and triangular lattices. We also construct the tau -function formulations and Darboux-Bäcklund transformations of these dynamics.