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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 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.

preprint2022arXivOpen access
Xiaoxue XuCewen CaoDa-jun Zhang
nlin.SI
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Xiaoxue XuCewen CaoDa-jun Zhang

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