## 14 Citations

### Tau function of the CKP hierarchy and nonlinearizable virasoro symmetries

- Mathematics
- 2013

We introduce a single tau function that represents the C-type Kadomtsev–Petviashvili (CKP) hierarchy in a generalized Hirota ‘bilinear’ equation. The actions on the tau function by additional…

### Bilinear Equation and Additional Symmetries for an Extension of the Kadomtsev–Petviashvili Hierarchy

- MathematicsMathematical Physics, Analysis and Geometry
- 2021

An extension of the Kadomtsev-Petviashvili (KP) hierarchy was considered in [J. Geom. Phys. 106 (2016), 327--341], which possesses a class of bi-Hamiltonian structures. In this paper, we represent…

### The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints

- Mathematics
- 2014

The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the…

### CMC hierarchy II: Non-commuting symmetries and affine Kac-Moody algebra

- Mathematics
- 2014

Continuing the previous work, we propose a further extension of the structure equation for a truncated CMC hierarchy by the non-commuting, truncated Virasoro algebra of non-local symmetries. Via a…

### Block algebra in two-component BKP and D type Drinfeld-Sokolov hierarchies

- Mathematics
- 2013

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…

### Block (or Hamiltonian) Lie symmetry of dispersionless D type Drinfeld-Sokolov hierarchy

- Mathematics
- 2014

In this paper, the dispersionless D type Drinfeld-Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this herarchy are…

### Addition Formulae of Discrete KP, q-KP and Two-Component BKP Systems*

- Mathematics
- 2016

In this paper, we construct the addition formulae for several integrable hierarchies, including the discrete KP, the q-deformed KP, the two-component BKP and the D type Drinfeld–Sokolov hierarchies.…

## References

SHOWING 1-10 OF 35 REFERENCES

### Virasoro Symmetries of the Extended Toda Hierarchy

- Mathematics
- 2003

We prove that the extended Toda hierarchy of [1] admits a nonabelian Lie algebra of infinitesimal symmetries isomorphic to half of the Virasoro algebra. The generators Lm, m≥−1 of the Lie algebra act…

### On additional symmetries of the KP hierarchy and Sato's Backlund transformation

- Mathematics
- 1993

A short proof is given to the fact that the additional symmetries of the KP hierarchy defined by their action on pseudodifferential operators according to Fuchssteiner-Chen-Lee-Lin-Orlov-Shulman…

### A remark on Kac–Wakimoto hierarchies of D-type

- Mathematics
- 2009

For the Kac–Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D(1)n, we compute the coefficients of the corresponding…

### On the Drinfeld–Sokolov Hierarchies of D Type

- Mathematics
- 2009

We extend the notion of pseudo-differential operators that are used to represent the Gelfand–Dickey hierarchies and obtain a similar representation for the full Drinfeld–Sokolov hierarchies of D n…

### Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type

- Mathematics
- 1982

### Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

- Mathematics
- 2001

We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the…

### Transformation Groups for Soliton Equations —Euclidean Lie Algebras and Reduction of the KP Hierarchy—

- Mathematics
- 1982

This is the last chapter of our series of papers [1], [3], [10], [11] on transformation groups for soliton equations. In [1] a link between the KdV (Korteweg de Vries) equation and the affine Lie…

### Simple singularities and integrable hierarchies

- Mathematics
- 2005

The paper [11] gives a construction of the total descendent potential corresponding to a semisimple Frobenius manifold. In [12], it is proved that the total descendent potential corresponding to K.…

### A Lax representation for the vertex operator and the central extension

- Mathematics
- 1995

Integrable hierarchies, viewed as isospectral deformations of an operatorL may admit symmetries; they are time-dependent vector fields, transversal to and commuting with the hierarchy and forming an…

### Additional symmetries for integrable equations and conformal algebra representation

- Mathematics
- 1986

AbstractWe present a regular procedure for constructing an infinite set of additional (spacetime variables explicitly dependent) symmetries of integrable nonlinear evolution equations (INEEs). In our…