Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lax operators   We define a Lax operator as a monic pseudodifferential operator $L(\partial)$
of order $N\geq 1$, such that the Lax equations $\dfrac{\partial
L(\partial)}{\partial t_k}=[(L^{\frac kN}(\partial))_+,L(\partial)]$ are
consistent and non-zero for infinitely many positive integers $k$. Consistency
of an equation means that its flow is defined by an evolutionary vector field.
In the present paper we demonstrate that the traditional theory of the KP and
the $N$-th KdV hierarchies holds for arbitrary scalar Lax operators.

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The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom