Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix extension of multidimensional dispersionless integrable
  hierarchies   We consistently develop a recently proposed scheme of matrix extension of
dispersionless integrable systems for the general case of multidimensional
hierarchies, concentrating on the case of dimension $d\geqslant 4$. We present
extended Lax pairs, Lax-Sato equations, matrix equations on the background of
vector fields and the dressing scheme. Reductions, construction of solutions
and connections to geometry are discussed. We consider separately a case of
Abelian extension, for which the Riemann-Hilbert equations of the dressing
scheme are explicitly solvable and give an analogue of Penrose formula in the
curved space.

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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
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The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
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The categories of this paper are: physics