## 22 Citations

### Flat Coordinates and Hidden Symmetry for Superintegrable Benenti Systems

- Mathematics
- 2007

In this talk I present the results from my paper Exact solvability of superintegrable Benenti systems, J. Math. Phys. 48 (2007), 052114.

### Lax Representations for Separable Systems from Benenti Class

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

In this paper we construct Lax pairs for St\"ackel systems with separation curves from so-called Benenti class. For each system of considered family we present an infinite family of Lax…

### Exact solvability of superintegrable Benenti systems

- Mathematics
- 2007

We establish quantum and classical exact solvability for two large classes of maximally superintegrable Benenti systems in n dimensions with arbitrarily large n. Namely, we solve the Hamilton-Jacobi…

### Non-Homogeneous Hydrodynamic Systems and Quasi-Stackel Hamiltonians

- Mathematics
- 2017

In this paper we present a novel construction of non-homogeneous hydrodynamic equations from what we call quasi-Stackel systems, that is non-commutatively integrable systems constructed from approp…

### Flat coordinates for flat St\"ackel systems

- Mathematics
- 2014

In this article we explicitely construct transformation bewteen separable and flat coordinates for flat St\"ackel systems and exploit the structre of these systems in flat coordinates. In the…

### Classical Integrable and Separable Hamiltonian Systems

- MathematicsQuantum versus Classical Mechanics and Integrability Problems
- 2019

In this chapter we introduce the concept of classical integrability of Hamiltonian systems and then develop the separability theory of such systems based on the notion of separation relations…

### Stäckel transform of Lax equations

- MathematicsStudies in Applied Mathematics
- 2020

We construct a map between Lax equations for pairs of Liouville integrable Hamiltonian systems related by a multiparameter Stäckel transform. Using this map, we construct Lax representation for a…

## References

SHOWING 1-10 OF 32 REFERENCES

### Maximal superintegrability of Benenti systems

- Mathematics
- 2005

For a class of Hamiltonian systems, naturally arising in the modern theory of separation of variables, we establish their maximal superintegrability by explicitly constructing the additional…

### A class of nonconservative Lagrangian systems on Riemannian manifolds

- Mathematics
- 2001

We generalize results of Rauch-Wojciechowski, Marciniak and Lundmark, concerning a class of nonconservative Lagrangian systems, from the Euclidean to the Riemannian case.

### Systematic Construction of Separable Systems with Quadratic in Momenta First Integrals

- Mathematics
- 2004

Liouville integrable separable systems with quadratic in momenta first integrals are considered. Particular attention is paid to the systems generated by the so-called special conformal Killing…

### On separability of bi-Hamiltonian chain with degenerated Poisson structures

- Mathematics
- 1998

Separability of bi-Hamiltonian finite-dimensional chains with two degenerated Poisson tensors, which have Pfaffian quasi-bi-Hamiltonian representation, is proved.

### From Stäckel systems to integrable hierarchies of PDE’s: Benenti class of separation relations

- Mathematics
- 2006

We propose a general scheme of constructing of soliton hierarchies from finite dimensional Stackel systems and related separation relations. In particular, we concentrate on the simplest class of…

### Exact solvability of superintegrable Benenti systems

- Mathematics
- 2007

We establish quantum and classical exact solvability for two large classes of maximally superintegrable Benenti systems in n dimensions with arbitrarily large n. Namely, we solve the Hamilton-Jacobi…

### Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation

- Mathematics
- 1997

The nonorthogonal separation of variables in the Hamilton–Jacobi equation corresponding to a natural Hamiltonian H=12gijpipj+V, with a metric tensor of any signature, is intrinsically characterized…

### RECIPROCAL TRANSFORMATIONS FOR ST ¨ ACKEL-RELATED LIOUVILLE INTEGRABLE SYSTEMS

- Mathematics
- 2006

We consider the Stackel transform, also known as the coupling-constant metamorphosis, which under certain conditions turns a Hamiltonian dynamical system into another such system and preserves the…

### Multi-Hamiltonian Theory of Dynamical Systems

- Physics
- 1998

Preliminary considerations elements of differential calculus for tensor fields the theory of Hamiltonian and bi-Hamiltonian systems lax representations of multi-Hamiltonian systems multi-Hamiltonian…