Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New non-linear equations and modular form expansion for double-elliptic
  Seiberg-Witten prepotential   Integrable N-particle systems have an important property that the associated
Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not
apply to the most interesting class of elliptic and double-elliptic systems.
Studying the commutativity conjecture for theta-functions on the families of
associated spectral curves, we derive some other non-linear equations for the
perturbative Seiberg-Witten prepotential, which turn out to have exactly the
double-elliptic system as their generic solution. In contrast with the WDVV
equations, the new equations acquire non-perturbative corrections which are
straightforwardly deducible from the commutativity conditions. We obtain such
corrections in the first non-trivial case of N=3 and describe the structure of
non-perturbative solutions as expansions in powers of the flat moduli with
coefficients that are (quasi)modular forms of the elliptic parameter.

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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph