Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical $N$-Reflection Equation and Gaudin Models   We introduce the notion of $N$-reflection equation which provides a large
generalization of the usual classical reflection equation describing integrable
boundary conditions. The latter is recovered as a special example of the $N=2$
case. The basic theory is established and illustrated with several examples of
solutions of the $N$-reflection equation associated to the rational and
trigonometric $r$-matrices. A central result is the construction of a Poisson
algebra associated to a non skew-symmetric $r$-matrix whose form is specified
by a solution of the $N$-reflection equation. Generating functions of
quantities in involution can be identified within this Poisson algebra. As an
application, we construct new classical Gaudin-type Hamiltonians, particular
cases of which are Gaudin Hamiltonians of $BC_L$-type .

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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th