# Central extensions of cotangent universal hierarchy: ()-dimensional bi-Hamiltonian systems

@article{Sergyeyev2008CentralEO, title={Central extensions of cotangent universal hierarchy: ()-dimensional bi-Hamiltonian systems}, author={Artur Sergyeyev and Blazej M. Szablikowski}, journal={Physics Letters A}, year={2008}, volume={372}, pages={7016-7023} }

## 21 Citations

### Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2019

The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions allowing the introducing of additional…

### Generalized Lie-algebraic structures related to integrable dispersionless dynamical systems and their application

- MathematicsJournal of Mathematical Sciences and Modelling
- 2018

Our review is devoted to Lie-algebraic structures and integrability properties of an interesting class of nonlinear dynamical systems called the dispersionless heavenly equations, which were…

### Lie-algebraic structure of Lax–Sato integrable heavenly equations and the Lagrange–d’Alembert principle

- Mathematics
- 2017

### The generalized centrally extended Lie algebraic structures and related integrable heavenly type equations

- Mathematics
- 2020

There are studied Lie-algebraic structures of a wide class of heavenly type non-linear integrable equations, related with coadjoint flows on the adjoint space to a loop vector field Lie algebra on…

### Classical R-matrix theory for bi-Hamiltonian field systems

- Mathematics
- 2009

This is a survey of the application of the classical R-matrix formalism to the construction of infinite-dimensional integrable Hamiltonian field systems. The main point is the study of bi-Hamiltonian…

### The Lax–Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure

- MathematicsEuropean Journal of Mathematics
- 2019

A Lie-algebraic approach to constructing the Lax–Sato integrable superanalogs of heavenly equations by use of the loop Lie algebra of superconformal vector fields on a 1| N -dimensional supertorus is…

### Complete Classification of Local Conservation Laws for Generalized Kuramoto-Sivashinsky Equation

- Mathematics
- 2021

For an arbitrary number of spatial independent variables we present a complete list of cases when the generalized Kuramoto–Sivashinsky equation admits nontrivial local conservation laws of any order,…

### Classical M. A. Buhl Problem, Its Pfeiffer–Sato Solutions, and the Classical Lagrange–D’Alembert Principle for the Integrable Heavenly-Type Nonlinear Equations

- Mathematics
- 2018

The survey is devoted to old and recent investigations of the classical M. A. Buhl problem of description of the compatible linear vector field equations and their general Pfeiffer and modern…

### Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky-Novikov Type Symmetry Algebras and Related Hamiltonian Operators

- MathematicsSymmetry
- 2018

It is shown that the Balinsky–Novikov type algebraic structures, obtained as a Hamiltonicity condition, are derivations on the Lie algebras naturally associated with differential toroidal loop alge bras.

### The dispersionless integrable systems and related conformal structure generating equations of mathematical physics

- Mathematics
- 2019

Based on the diffeomorphism group vector fields on the complexified torus and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems, describing conformal…

## References

SHOWING 1-10 OF 29 REFERENCES

### Recursion operators and bi-Hamiltonian structures in multidimensions. I

- Mathematics
- 1988

The algebraic properties of exactly solvable evolution equations in one spatial and one temporal dimensions have been well studied. In particular, the factorization of certain operators, called…

### Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability

- Mathematics
- 2004

A (d+1)-dimensional dispersionless PDE is said to be integrable if its n-component hydrodynamic reductions are locally parametrized by (d−1)n arbitrary functions of one variable. The most important…

### Applications of lie groups to differential equations

- Mathematics
- 1986

1 Introduction to Lie Groups.- 1.1. Manifolds.- Change of Coordinates.- Maps Between Manifolds.- The Maximal Rank Condition.- Submanifolds.- Regular Submanifolds.- Implicit Submanifolds.- Curves and…

### Towards classification of -dimensional integrable equations. Integrability conditions I

- Mathematics
- 1998

In this paper we attempt to extend the symmetry approach (well developed in the case of (1 + 1)-dimensional equations) to the (2 + 1)-dimensional case. Presence of nonlocal terms in symmetries and…

### A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields

- Mathematics
- 2008

We study a hierarchy of integrable partial differential equations in 2 + 1 dimensions arising from the commutation of 2 - dimensional vector fields, and we construct the formal solution of the…

### A hierarchy of integrable partial differential equations in 2+1 dimensions associated with one-parameter families of one-dimensional vector fields

- Mathematics
- 2007

We introduce a hierarchy of integrable partial differential equations in 2+1 dimensions arising from the commutation of one-parameter families of vector fields, and we construct the formal solution…

### Hamiltonian theory over noncommutative rings and integrability in multidimensions

- Mathematics
- 1992

A generalization of the Adler–Gel’fand–Dikii scheme is used to generate bi‐Hamiltonian structures in two spatial dimensions. In order to implement this scheme, a Hamiltonian theory is built over a…

### Lie algebraic approach to the construction of (2+1)-dimensional lattice-field and field integrable Hamiltonian equations

- Mathematics
- 2001

Two different methods for the construction of (2+1)-dimensional integrable lattice-field and field Hamiltonian dynamical systems are presented. The first method is based on the so-called central…

### Universal Models of Soliton Hierarchies

- Mathematics
- 2003

We consider commutativity equations and a related new model similar to the Kadomtsev–Petviashvili equation in the Sato theory. Integration of this model equation with three independent variables is…