The Hirota equation over finite fields. Algebro-geometric approach and multisoliton solutions

Abstract

We consider the Hirota equation (the discrete analog of the generalized Toda system) over a finite field. We present the general algebro-geometric method of construction of solutions of the equation. As an example we construct analogs of the multisoliton solutions for which the wave functions and the $\tau$-function can be found using rational functions. Within the class of multisoliton solutions we isolate generalized breather-type solutions which have no direct counterparts in the complex field case.

arXiv comment18 pages

References in corpus (8)

• Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations
• Multidimensional Quadrilateral Lattices are Integrable
• Transformations of Quadrilateral Lattices
• Geometric Discretisation of the Toda System
• Elliptic solutions to difference non-linear equations and related many-body problems
• The symmetric, D-invariant and Egorov reductions of the quadrilateral lattice
• Quadratic reductions of quadrilateral lattices
• Discrete analogs of the Darboux-Egoroff metrics

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