2009/03/18 by P. D. Xenitidis, P D Xenitidis, V. G. Papageorgiou +1 · 28 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Homogeneous space #Lattice (music) #Lax pair #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Symmetry (geometry) #Toda lattice #Type (biology) #nlin.SI
paper · pdf · doi:10.1088/1751-8113/42/45/454025
published in Journal of Physics A Mathematical and Theoretical 42(45), 454025 (Institute of Physics) · 12 pages, submitted to the special issue on "Symmetries and Integrability of Difference Equations" of J. Phys. A: Math. Theor
arxiv created 2009/03/18 · openalex publication_date 2009/10/27 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We study the deformations of the H equations, presented recently by Adler, Bobenko and Suris, which are naturally defined on a black–white lattice. For each one of these equations, two different three-leg forms are constructed, leading to two different discrete Toda-type equations. Their multidimensional consistency leads to Bäcklund transformations relating different members of this class as well as to Lax pairs. Their symmetry analysis is presented yielding infinite hierarchies of generalized symmetries.