Building Abelian functions with generalised Hirota operators

Details Building Abelian functions with generalised Hirota operators Building Abelian functions with generalised Hirota operators

2012-03-15

arxiv.org/abs/1203.3409v1

Physics

Mathematical Physics

35 pages

Scientific paper

We consider symmetric generalisations of Hirota's bilinear operator. We demonstrate some of the properties of these operators, focusing on how they may be used to build new classes of Abelian (multiply periodic) functions. We give explicit formulae for the multiple applications of the operators, define infinite sequences of Abelian functions of a given pole structure and deduce some of their properties. We present several explicit examples of vector space bases for Abelian functions obtained using the new results, revealing previously unseen similarities between the bases of functions associated to curves of the same genus.

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