Related papers: The nonstandard constrained KP hierarchy and the g…
By generalizing the Miura transformation for $\Ww_N$ to other classical $\Ww$ algebras obtained by hamiltonian reduction, we find realisations of these algebras in terms of relatively simple non-abelian current algebras, e.g.…
Using the bilinear formalism, we consider multicomponent and matrix modified KP hierarchies. The main tool is the bilinear identity for the tau-function which is realized as an expectation value of a Clifford group element composed from…
Following the techniques of M. Sato (see \cite{Sa}), a generalization of the KP hierarchy for more than one variable is proposed. An approach to the classification of solutions and a method to construct algebraic solutions is also offered.
In this paper, we mainly investigate Lax structure and tau function for the large BKP hierarchy, which is also known as Toda hierarchy of B type, or Hirota--Ohta--coupled KP hierarchy, or Pfaff lattice. Firstly, the large BKP hierarchy can…
The V-algebras are the non-local matrix generalization of the well-known W-algebras. Their classical realizations are given by the second Poisson brackets associated with the matrix pseudodifferential operators. In this paper, by using the…
Recent work on a free field realization of the Hamiltonian structures of the classical KP hierarchy and of its flows is reviewed. It is shown that it corresponds to a reduction of KP to the NLS system. (Talk given by D.A.D. at the NSERC-CAP…
Restricting a linear system for the KP hierarchy to those independent variables t\_n with odd n, its compatibility (Zakharov-Shabat conditions) leads to the "odd KP hierarchy". The latter consists of pairs of equations for two dependent…
Based on the Orlov and Shulman's M operator, the additional symmetries and the string equation of the CKP hierarchy are established, and then the higher order constraints on $L^l$ are obtained. In addition, the generating function and some…
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting $\W$-algebra is a…
We introduce a generalisation of the KP hierarchy, closely related to the cyclic quiver and the Cherednik algebra $H_k(\mathbb Z_m)$. This hierarchy depends on $m$ parameters (one of which can be eliminated), with the usual KP hierarchy…
It is shown that the matrix KP hierarchy can yield new integrable equations in $(2+1)$-dimensions along with the corresponding Lax pair. For particular gauge choice this may result derivative and also a higher order nonlinear extension of…
Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is…
In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators $L=p^n+\sum_{j=-\infty}^{n-1}u_j p^j$. The reduction of the Poisson…
The construction of negative grade KdV hierarchy is proposed in terms of a Miura-gauge transformation. Such gauge transformation is employed within the zero curvature representation and maps the Lax operator of the mKdV into its couterpart…
We investigate self-similar solutions of the extended discrete KP hierarchy. It is shown that corresponding ansatzes lead to purely discrete equations with dependence on some number of parameters together with equations governing…
Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy…
In this paper, we investigated four applications of the gauge transformation for the BKP hierarchy. Firstly, it is found that the orbit of the gauge transformation for the constrained BKP hierarchy defines a special $(2 +1)$-dimensional…
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…
The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction $\{\Phi_i,\Psi_i \}$ are presented…
Constrained KP and super-KP hierarchies of integrable equations (generalized NLS hierarchies) are systematically produced through a Lie algebraic AKS-matrix framework associated to the homogeneous grading. The role played by different…