Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new approach to deformation equations of noncommutative KP hierarchies   Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP)
hierarchy, we start with a quite general hierarchy of linear ordinary
differential equations in a space of matrices and derive from it a matrix
Riccati hierarchy. The latter is then shown to exhibit an underlying 'weakly
nonassociative' (WNA) algebra structure, from which we can conclude, refering
to previous work, that any solution of the Riccati system also solves the
potential KP hierarchy (in the corresponding matrix algebra). We then turn to
the case where the components of the matrices are multiplied using a
(generalized) star product. Associated with the deformation parameters, there
are additional symmetries (flow equations) which enlarge the respective KP
hierarchy. They have a compact formulation in terms of the WNA structure. We
also present a formulation of the KP hierarchy equations themselves as
deformation flow equations.

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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
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The categories of this paper are: stat
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg