A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy

  title={A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy},
  author={Oleksandr Chvartatskyi and Yuriy Sydorenko},
  journal={Journal of Mathematical Physics},
We introduce a new bidirectional generalization of (2+1)-dimensional k-constrained Kadomtsev-Petviashvili (KP) hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes (2+1)-dimensional k-cKP hierarchy, (tA, τB) and (γA, σB) 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 Davey-Stewartson (DS) systems, (2+1)-dimensional modified Korteweg-de Vries… 
Darboux Transformations for (2 + 1)-Dimensional Extensions of the KP Hierarchy
New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of (2 + 1)dimensional integrable equations, including the DS-III
Additional Reductions in the K -Constrained Modified KP Hierarchy
Additional reductions are proposed for the modified k-constrained KP hierarchy. As a result, we obtain generalizations of Kaup–Broer system, Korteweg–de-Vries equation, and a modification of the


Hierarchy of the Kadomtsev-Petviashvili equations under nonlocal constraints: Many-dimensional generalizations and exact solutions of reduced system
We present a spatially two-dimensional generalization of the hierarchy of Kadomtsev-Petviashvili equations under nonlocal constraints (the so-called 2-dimensionalk-constrained KP-hierarchy, briefly
Matrix generalizations of integrable systems with Lax integro-differential representations
We present (2+1)-dimensional generalizations of the k-constrained Kadomtsev-Petviashvili (k-cKP) hierarchy and corresponding matrix Lax representations that consist of two integro-differential
Solutions for the vector k‐constrained KP hierarchy
A class of (1+1)‐dimensional integrable systems which are constrained from the Kadomtsev–Petviashvili (KP) hierarchy is studied. The bilinear equations of these integrable systems are shown first,
Constrained KP Hierarchies: Additional Symmetries, Darboux–Bäcklund Solutions and Relations to Multi-Matrix Models
This paper provides a systematic description of the interplay between a specific class of reductions denoted as \cKPrm ($r,m \geq 1$) of the primary continuum integrable system -- the
Multicomponent integrable reductions in the Kadomtsev–Petviashvilli hierarchy
New types of reductions of the Kadomtsev–Petviashvili (KP) hierarchy are considered on the basis of Sato’s approach. Within this approach the KP hierarchy is represented by infinite sets of equations
A New (γ A , σ B )-Matrix KP Hierarchy and Its Solutions
A new (γA, σB)-matrix KP hierarchy with two time series γA and σB, which consists of γA-flow, σB-flow and mixed γA and σB-evolution equations of eigenfunctions, is proposed. The reduction and
Integrable equations in (2+1) dimensions associated with symmetric and homogeneous spaces
Generalizations of the N‐wave, Davey–Stewartson, and Kadomtsev–Petviashvili equations associated with homogeneous and symmetric spaces are presented. These equations are (2+1)‐dimensional
Constraints of the Kadomtsev-Petviashvili hierarchy
For the Kadomtsev–Petviashvili (KP) hierarchy constructed in terms of the famous Sato theory, a ‘‘k constraint’’ is proposed that leads the hierarchy to the nonlinear system involving a finite number
A new extended matrix KP hierarchy and its solutions
Starting from the matrix KP hierarchy and adding a new τB flow, we obtain a new extended matrix KP hierarchy and its Lax representation with the symmetry constraint on squared eigenfunctions taken
Constraints of the 2+1 dimensional integrable soliton systems
The authors show that the linear systems associated with some integrable hierarchies of the soliton equations in 2+1 dimensions can be constrained to integrable hierarchies in 1+1 dimensions such