Algebro-geometric solutions to the lattice potential modified Kadomtsev–Petviashvili equation. (16th September 2022)

• Record Type: Journal Article
• Authors: Xu, Xiaoxue; Cao, Cewen; Zhang, Da-jun
• Is Part Of: Journal of physics. Volume 55:Number 37(2022)
• Publication Date: 2022-09-16
• Subjects: lattice potential modified Kadomtsev–Petviashvili equation -- algebro-geometric solution -- Kaup–Newell spectral problem -- Baker–AkhiezerAkhiezer function; 35Q51 -- 37K60 -- 39A36; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac8252
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Algebro-geometric solutions of the lattice potential modified Kadomtsev–Petviashvili (lpmKP) equation are constructed. A Darboux transformation of the Kaup–Newell spectral problem is employed to generate a Lax triad for the lpmKP equation, as well as to define commutative integrable symplectic maps which generate discrete flows of eigenfunctions. These maps share the same integrals with the finite-dimensional Hamiltonian system associated to the Kaup–Newell spectral problem. We investigate asymptotic behaviors of the Baker–Akhiezer functions and obtain their expression in terms of Riemann theta function. Finally, algebro-geometric solutions for the lpmKP equation are reconstructed from these Baker–Akhiezer functions.