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Algebro-Geometric Solution of the Discrete KP Equation over a Finite Field out of a Hyperelliptic Curve

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Abstract

We transfer the algebro-geometric method of construction of solutions of the discrete KP equation to the finite field case. We emphasize the 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.

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Authors and Affiliations

  1. Instytut Geofizyki PAN, ul. Ksieçcia Janusza 64, 01-452, Warszawa, Poland

    Mariusz Białecki

  2. Wydział Matematyki i Informatyki, Uniwersytet Warmińsko–Mazurski, ul. Zołnierska 14A, 10-561, Olsztyn, Poland

    Adam Doliwa

Authors
  1. Mariusz Białecki
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  2. Adam Doliwa
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Correspondence to Adam Doliwa.

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Communicated by L. Takhtajan

Acknowledgement The paper was partially supported by the University of Warmia and Mazury in Olsztyn under the grant 522-1307-0201 and by KBN grant 2 P03B 12622.

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Białecki, M., Doliwa, A. Algebro-Geometric Solution of the Discrete KP Equation over a Finite Field out of a Hyperelliptic Curve. Commun. Math. Phys. 253, 157–170 (2005). https://doi.org/10.1007/s00220-004-1207-3

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