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

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

2002-11-25

arxiv.org/abs/nlin/0211043v1

J. Phys. A: Math. Gen. 36 (2003) 4827-4839

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages

Scientific paper

10.1088/0305-4470/36/17/309

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.

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