2024/12/17 by Baoqiang Xia, Xia, Baoqiang
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2412.12461
openalex publication_date 2024/12/17 · openalex created_date 2024/12/19 · openalex updated_date 2026/07/28
We investigate the complete integrability of soliton equations with shifted nonlocal reductions under the rapidly decreasing boundary conditions. The illustrative examples we choose are the Ablowitz-Ladik (AL) system and the Ablowitz-Kaup-Newell-Segur (AKNS) system. For this two models with the space and space-time shifted nonlocal reductions, we establish the complete integrability of the resulting nonlocal systems by an explicit construction of the variables of action-angle type from the corresponding scattering data. Moreover, we find that the time shifted nonlocal reductions, unlike the space and space-time shifted ones, are not compatible with the Poisson bracket relations of the corresponding scattering data in the presence of the discrete spectrum.