Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new bidirectional generalization of (2+1)-dimensional matrix
  k-constrained KP hierarchy   We introduce a new bidirectional generalization of (2+1)-dimensional
k-constrained KP hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes
(2+1)-dimensional k-cKP hierarchy, $(t_A,\tau_B)$ and $(\gamma_A,\sigma_B)$
matrix hierarchies. (2+1)-BDk-cKPH contains a new matrix (1+1)-k-constrained KP
hierarchy. Some members of (2+1)-BDk-cKPH are also listed. In particular, it
contains matrix generalizations of DS systems, (2+1)-dimensional modified
Korteweg-de Vries equation and the Nizhnik equation. (2+1)-BDk-cKPH also
includes new matrix (2+1)-dimensional generalizations of the Yajima-Oikawa and
Melnikov systems. Binary Darboux Transformation Dressing Method is also
proposed for construction of exact solutions for equations from (2+1)-BDk-cKPH.
As an example the exact form of multi-soliton solutions for vector
generalization of the Davey-Stewartson system is given.

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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph