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

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...

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Veröffentlicht in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2022-09, Vol.55 (37), p.375201
Hauptverfasser: Xu, Xiaoxue, Cao, Cewen, Zhang, Da-jun
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Sprache:eng
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algebro-geometric solution
Baker–AkhiezerAkhiezer function
Kaup–Newell spectral problem
lattice potential modified Kadomtsev–Petviashvili equation
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Cao, Cewen
Zhang, Da-jun
description 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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subjects algebro-geometric solution
Baker–AkhiezerAkhiezer function
Kaup–Newell spectral problem
lattice potential modified Kadomtsev–Petviashvili equation
title Algebro-geometric solutions to the lattice potential modified Kadomtsev–Petviashvili equation
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