  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.
