# Generalized KP hierarchy: Mbius symmetry, symmetry constraints and CalogeroMoser system

@article{Bogdanov1999GeneralizedKH, title={Generalized KP hierarchy: Mbius symmetry, symmetry constraints and CalogeroMoser system}, author={L. V. Bogdanov and B. G. Konopelchenko}, journal={Physica D: Nonlinear Phenomena}, year={1999} }

## 6 Citations

### Hirota Difference Equation and Darboux System: Mutual Symmetry

- MathematicsSymmetry
- 2019

We considered the relation between two famous integrable equations: The Hirota difference equation (HDE) and the Darboux system that describes conjugate curvilinear systems of coordinates in R 3 . We…

### Symmetries of the Hirota Difference Equation

- Mathematics
- 2017

Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent…

### Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy

- Mathematics, Physics
- 2001

Trigonometric non-isospectral flows are defined for KP hierarchy. It is demonstrated that symmetry constraints of KP hierarchy associated with these flows give rise to trigonometric Calogero-Moser…

### Hirota difference equation and a commutator identity on an associative algebra

- Mathematics
- 2011

. In earlier papers of the author it was shown that some simple commutator identities on an associative algebra generate integrable nonlinear equations. Here, this observation is generalized to the…

### Hirota difference equation: Inverse scattering transform, darboux transformation, and solitons

- Mathematics
- 2014

We consider the direct and inverse problems for the Hirota difference equation. We introduce the Jost solutions and scattering data and describe their properties. In a special case, we show that the…

### 3-Algebraic structures of the quantum Calogero-Moser model

- Mathematics
- 2014

We investigate the quantum Calogero-Moser model and reveal its hidden symmetries, i.e., the $W_{1+\infty}$ and Virasoro-Witt 3-algebras. In the large $N$ limit, we note that these two infinite…

## References

SHOWING 1-10 OF 17 REFERENCES

### Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy

- Mathematics
- 1996

An analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is proposed. It starts with the generalized Hirota identity for the…

### Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies

- Mathematics
- 1997

An analytic-bilinear approach for the construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows…

### Möbius invariant integrable lattice equations associated with KP and 2DTL hierarchies

- Mathematics
- 1999

### 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…

### THE PAINLEVE PROPERTY FOR PARTIAL DIFFERENTIAL EQUATIONS. II. BACKLUND TRANSFORMATION, LAX PAIRS, AND THE SCHWARZIAN DERIVATIVE

- Mathematics
- 1983

In this paper we investigate the Painleve property for partial differential equations. By application to several well‐known partial differential equations (Burgers, KdV, MKdV, Bousinesq, higher‐order…

### Generalized Hirota bilinear identity and integrable q-difference and lattice hierarchies

- Mathematics
- 1994

### New reductions of the Kadomtsev–Petviashvili and two‐dimensional Toda lattice hierarchies via symmetry constraints

- Mathematics
- 1992

New types of reductions of the Kadomtsev–Petviashvili (KP) hierarchy and the two‐dimensional Toda lattice (2DTL) hierarchy are considered on the basis of Sato’s approach. Within this approach these…

### Nonlinear partial differential equations in applied science

- Nonlinear partial differential equations in applied science
- 1981