On trilinear and quadrilinear equations associated with the lattice Gel'fand-Dikii hierarchy

Autor:	van der Kamp, P. H., Nijhoff, F. W., McLaren, D. I., Quispel, G. R. W
Rok vydání:	2024
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	Introduced in 2012, by Zhang, Zhao, and Nijhoff, the trilinear Boussinesq equation is the natural form of the equation for the $\tau$-function of the lattice Boussinesq system. In this paper we study various aspects of this equation: its highly nontrivial derivation from the bilinear lattice AKP equation under dimensional reduction, a quadrilinear dual lattice equation, conservation laws, and periodic reductions leading to higher-dimensional integrable maps and their Laurent property. Furthermore, we consider a higher Gel'fand-Dikii lattice system, its periodic reductions and Laurent property. As a special application, from both a trilinear Boussinesq recurrence as well as a higher Gel'fand-Dikii system of three bilinear recurrences, we establish Somos-like integer sequences. Comment: 13 pages, 5 figures, Submitted to a special issue devoted to the celebration of 120 years from the day of birth of the famous Soviet mathematician A. Kolmogorov
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.11175 Zobrazit plný text záznamu View this record from Arxiv