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

Adam Doliwa·Mariusz Bialecki·Pawel Klimczewski
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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 $τ$-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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Adam Doliwa, Mariusz Bialecki, Pawel Klimczewski. 2002-11-25. The Hirota equation over finite fields. Algebro-geometric approach and multisoliton solutions. https://doi.org/10.1088/0305-4470%2F36%2F17%2F309

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