Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher analogues of the discrete-time Toda equation and the
  quotient-difference algorithm   The discrete-time Toda equation arises as a universal equation for the
relevant Hankel determinants associated with one-variable orthogonal
polynomials through the mechanism of adjacency, which amounts to the inclusion
of shifted weight functions in the orthogonality condition. In this paper we
extend this mechanism to a new class of two-variable orthogonal polynomials
where the variables are related via an elliptic curve. This leads to a `Higher
order Analogue of the Discrete-time Toda' (HADT) equation for the associated
Hankel determinants, together with its Lax pair, which is derived from the
relevant recurrence relations for the orthogonal polynomials. In a similar way
as the quotient-difference (QD) algorithm is related to the discrete-time Toda
equation, a novel quotient-quotient-difference (QQD) scheme is presented for
the HADT equation. We show that for both the HADT equation and the QQD scheme,
there exists well-posed $s$-periodic initial value problems, for almost all
$\s\in\Z^2$. From the Lax-pairs we furthermore derive invariants for
corresponding reductions to dynamical mappings for some explicit examples.

33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph