Algebro-geometric solutions to the lattice potential modified Kadomtsev–Petviashvili equation. (16th September 2022) - Xu, Xiaoxue; Cao, Cewen; Zhang, Da-jun
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.