Algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve

Abstract

We transfer the algebro-geometric method of construction of solutions of the discrete KP equation to the finite field case. We emphasize role of the Jacobian of the underlying algebraic curve in construction of the solutions. We illustrate in detail the procedure on example of a hyperelliptic curve.

14 pages; some typos corrected

References in corpus (2)

• Elliptic solutions to difference non-linear equations and related many-body problems
• The Hirota equation over finite fields. Algebro-geometric approach and multisoliton solutions

Cited by in corpus (14)

• The B-quadrilateral lattice, its transformations and the algebro-geometric construction
• The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction
• From deterministic cellular automata to coupled map lattices
• Analytic approach to stochastic cellular automata: exponential and inverse power distributions out of Random Domino Automaton
• Integrable Systems and Discrete Geometry
• Integrable 1D Toda cellular automata
• Darboux transformations for linear operators on two dimensional regular lattices
• Hirota equation and the quantum plane
• On pattern structures of the N-soliton solution of the discrete KP equation over a finite field
• Geometric algebra and quadrilateral lattices
• Non-autonomous multidimensional Toda system and multiple interpolation problem
• Quadrangular sets in projective line and in Moebius space, and geometric interpretation of the non-commutative discrete Schwarzian Kadomtsev-Petviashvili equation
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps
• Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations