Integrable equations and their evolutions based on intrinsic geometry of Riemann spaces.
Integrable Hamiltonian systems on Lie groups: Kowalewski type.
Integrable hierarchies and the modular class
It is well-known that the Poisson-Nijenhuis manifolds, introduced by Kosmann-Schwarzbach and Magri form the appropriate setting for studying many classical integrable hierarchies. In order to define the hierarchy, one usually specifies in addition to the Poisson-Nijenhuis manifold a bi-hamiltonian vector field. In this paper we show that to every Poisson-Nijenhuis manifold one can associate a canonical vector field (no extra choices are involved!) which under an appropriate assumption defines an...
Integrable string models in terms of chiral invariants of groups.
Integrable systems and group actions
The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.
Integrable systems and moduli spaces of rank two vector bundles on a non-hyperelliptic genus 3 curve
We use the methods that were developed by Adler and van Moerbeke to determine explicit equations for a certain moduli space, that was studied by Narasimhan and Ramanan. Stated briefly it is, for a fixed non-hyperelliptic Riemann surface of genus , the moduli space of semi-stable rank two bundles with trivial determinant on . They showed that it can be realized as a projective variety, more precisely as a quartic hypersurface of , whose singular locus is the Kummer variety of . We first construct...
Integrable systems, Poisson pencils, and hyperelliptic Lax pairs
Intertwining symmetry algebras of quantum superintegrable systems.
Invariant varieties of periodic points for the discrete Euler top.
Isometric immersions and the generalized Laplace and elliptic sinh-Gordon equations.
Isometric immersions of space forms and soliton theory.
Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials
In this paper, we consider the natural complex Hamiltonian systems with homogeneous potential , , of degree . The known results of Morales and Ramis give necessary conditions for the complete integrability of such systems. These conditions are expressed in terms of the eigenvalues of the Hessian matrix calculated at a non-zero point , such that . The main aim of this paper is to show that there are other obstructions for the integrability which appear if the matrix is not diagonalizable....
Kac-Moody groups and integrability of soliton equations.
L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices
We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.
Laurent polynomials and superintegrable maps.
Lax equation representation of certain completely integrable systems
Limit matrices for the Toda flow and periodic flags for loop groups.
Linearising two-dimensional integrable systems and the construction of action-angle variables.
Liouville integrability of geometric variational problems.
Metric with ergodic geodesic flow is completely determined by unparameterized geodesics.