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}
}

Hirota Difference Equation and Darboux System: Mutual Symmetry

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

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

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

. 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

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

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

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

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

Additional symmetries for integrable equations and conformal algebra representation

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

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

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

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

ORLOV

Nonlinear partial differential equations in applied science

  • Nonlinear partial differential equations in applied science
  • 1981