Related papers: Quantum torus symmetries of multicomponent modifie…
In this paper, we construct the Virasoro type additional symmetries of a kind of constrained multi-component KP hierarchy and give the Virasoro flow equation on eigenfunctions and adjoint eigenfunctions. It can also be seen that the…
In this paper, we construct a series of additional flows of the CKP hierarchy and the multi-component CKP hierarchy and these flows constitute a N-folds direct product of the positive half of the quantum Torus symmetry. Comparing to the…
In this paper, we construct the quantum Torus symmetry of the KP hierarchy and further derive the quantum torus constraint on the tau function of the KP hierarchy. That means we give a nice representation of the quantum Torus Lie algebra in…
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…
In this article, we will construct the additional perturbative quantum torus symmetry of the dispersionless BKP hierarchy basing on the $W_{\infty}$ infinite dimensional Lie symmetry. These results show that the complete quantum torus…
In this paper, we defined a new multi-component BKP hierarchy which takes values in a commutative subalgebra of $gl(N,\mathbb C)$. After this, we give the gauge transformation of this commutative multi-component BKP (CMBKP) hierarchy.…
In this paper, we construct a new even constrained B(C) type Toda hierarchy and derive its B(C) type Block type additional symmetry. Also we generalize the B(C) type Toda hierarchy to the $N$-component B(C) type Toda hierarchy which is…
In this paper, we construct the additional symmetries of one-component constrained discrete KP (cdKP) hierarchy, and then prove that the algebraic structure of the symmetry flows is the positive half of Virasoro algebra.
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…
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…
Modified Toda hierarchy is a two-component generalization of the 1st modified KP hierarchy, which has been widely applied to analyze constraints of the Toda hierarchy, including the B--Toda and C--Toda hierarchies. In this paper, we…
We develop a formalism of multicomponent BKP hierarchies using elementary geometry of spinors. The multicomponent KP and the modified KP hierarchy (hence all their reductions like KdV, NLS, AKNS or DS) are reductions of the multicomponent…
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…
A KP-mKP hierarchy was introduced recently via pseudo-differential operators containing two derivations. In this paper, for the KP-mKP hierarchy we derive a class of (differential) Fay identities and construct a series of additional…
An explanation for the so-called constrained hierarhies is presented by linking them with the symmetries of the KP hierarchy. While the existence of ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP hierarchy to…
In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
In this paper, we mainly study the additional symmetry and $\tau$ functions of a multi-component Gelfand-Dickey hierarchy which includes many classical integrable systems, such as the multi-component KdV hierarchy and the multi-component…
The constrained Modified KP hierarchy is considered from the viewpoint of modification. It is shown that its second Poisson bracket, which has a rather complicated form, is associated to a vastly simpler bracket via Miura-type map. The…
By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are taken as an illustrative example: new…
We investigate the structure of representations of the (positive half of the) Virasoro algebra and situations in which they decompose as a tensor product of Lie algebra representations. As an illustration, we apply these results to the…