2020/07/09 by Cewen Cao, Cao, Cewen, Xiaoxue Xu +3
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2007.04721
openalex publication_date 2020/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper presents an approach to derive finite genus solutions to the lattice potential Kadomtsev-Petviashvili (lpKP) equation introduced by F.W. Nijhoff, et al. This equation is rederived from compatible conditions of three replicas of the discrete ZS-AKNS spectral problem, which is a Darboux transformation of the continuous ZS-AKNS spectral problem. With the help of these links and by means of the so called nonlinearization technique and Liouville platform, finite genus solutions of the lpKP equation are derived. Semi-discrete potential KP equations with one and two discrete arguments, respectively, are also discussed.