Discrete Dubrovin Equations and Separation of Variables for Discrete Systems

F. W. Nijhoff

doi:10.1016/s0960-0779(98)00264-1

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arXiv · solv-int/9907015

Discrete Dubrovin Equations and Separation of Variables for Discrete Systems

F. W. Nijhoff

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Abstract

A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of finite-gap integration. The parametrisation of the solutions in terms of Abelian functions of Kleinian type (i.e. the higher-genus analogues of the Weierstrass elliptic functions) is discussed as well as the connections with the method of separation of variables.

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F. W. Nijhoff. 1999-07-15. Discrete Dubrovin Equations and Separation of Variables for Discrete Systems. https://doi.org/10.1016/s0960-0779(98)00264-1

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