Algebro-geometric solutions to the lattice potential modified Kadomtsev--Petviashvili equation
Xiaoxue Xu,
Cewen Cao,
Da-jun Zhang
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… Show more
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