2013/11/27 by S. Konstantinou-Rizos, Konstantinou-Rizos, Sotiris
Computer Science · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1311.7019
openalex publication_date 2013/11/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It is well known that, given a Yang-Baxter map, there is a hierarchy of commuting transfer maps, which arise out of the consideration of initial value problems. In this paper, we show that one can construct invariants of the transfer maps corresponding to the n-periodic initial value problem on the two-dimensional lattice, using the same generating function that is used to produce invariants of the Yang-Baxter map itself. Moreover, we discuss the Liouville integrability of these transfer maps. Finally, we consider four-dimensional Yang-Baxter maps corresponding to the nonlinear Schrödinger (NLS) equation and the derivative nonlinear Schrödinger (DNLS) equation which have recently appeared. We show that the associated transfer maps are completely integrable.