Algebro-geometric solutions to the lattice potential modified Kadomtsev–Petviashvili equation

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