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arXiv · 2111.10775

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

Xiaoxue Xu·Cewen Cao·Da-jun Zhang
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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.

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Xiaoxue Xu, Cewen Cao, Da-jun Zhang. 2021-11-21. Algebro-geometric solutions to the lattice potential modified Kadomtsev--Petviashvili equation. https://doi.org/10.1088/1751-8121%2Fac8252

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