Related papers: Constrained KP Models as Integrable Matrix Hierarc…
We illustrate the basic notions of {\em additional non-isospectral symmetries} and their interplay with the discrete {\em \DB transformations} of integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili} (\cKP)…
We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models ${\sl cKP}_{R,M}$, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an…
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.…
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 Kadomtsev-Petviashvili ({\sf KP}) hierarchy and discrete…
This work consist of two interrelated parts. First, we derive massive gauge-invariant generalizations of geometric actions on coadjoint orbits of arbitrary (infinite-dimensional) groups $G$ with central extensions, with gauge group $H$…
Additional non-isospectral symmetries are formulated for the constrained Kadomtsev-Petviashvili (\cKP) integrable hierarchies. The problem of compatibility of additional symmetries with the underlying constraints is solved explicitly for…
The $p\times p$ matrix version of the $r$-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra…
In this paper, we study two generalized constrained integrable hierarchies, which are called the $c$-$k$ constrained KP and BKP hierarchies. The Fermionic picture of the $c$-$k$ constrained KP hierarchy is given. We give some solutions for…
We present an affine $sl (n+1)$ algebraic construction of the basic constrained KP hierarchy. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax…
The algebraic structures of integrable hierarchies play an important role in the study of soliton equations. In this paper, we use splitting theory to give a matrix representation of a constrained CKP hierarchy, which can be considered as a…
This paper is devoted to the systematic study of additional (non- isospectral) symmetries of constrained (reduced) supersymmetric integrable hierarchies of KP type- the so called SKP_(R;M_B,M_F) models. The latter are supersymmetric…
We introduce a new generalization of matrix (1+1)-dimensional k-constrained KP hierarchy. The new hierarchy contains matrix generalizations of stationary DS systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik…
Toda lattice hierarchy and the associated matrix formulation of the $2M$-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working…
In this paper, we construct the additional symmetries of the supersymmetric BKP(SBKP) hierarchy. These additional flows constitute a B type $SW_{1+\infty}$ Lie algebra because of the B type reduction of the supersymmetric BKP hierarchy.…
We derive sufficient conditions under which the ``second'' Hamiltonian structure of a class of generalized KdV-hierarchies defines one of the classical $\cal W$-algebras obtained through Drinfel'd-Sokolov Hamiltonian reduction. These…
We show that the 2-matrix string model corresponds to a coupled system of $2+1$-dimensional KP and modified KP ($\KPm$) integrable equations subject to a specific ``symmetry'' constraint. The latter together with the Miura-Konopelchenko map…
We construct the vertex operator representation for the Affine Kac-Moody $SL(M+K+1)$ algebra, which is relevant for the construction of the soliton solutions of the constrained KP hierarchies. The oscillators involved in the vertex operator…
We construct generalized additional symmetries of a two-component BKP hierarchy defined by two pseudo-differential Lax operators. These additional symmetry flows form a Block type algebra with some modified(or additional) terms because of a…
We discuss the integrable hierarchies that appear in multi--matrix models. They can be envisaged as multi--field representations of the KP hierarchy. We then study the possible reductions of this systems via the Dirac reduction method by…
Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local reductions of Hamiltonian flows generated by monodromy invariants on the dual of a loop algebra. Following earlier work of De Groot et al, reductions based upon…