Related papers: Integrable systems with symmetries: toric, semitor…
Quantum mechanical systems with some degree of complexity due to multiple scattering behave as if their Hamiltonians were random matrices. Such behavior, while originally surmised for the interacting many-body system of highly excited…
This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…
Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of…
The purpose of this material is to review the Adler Kostant Symes scheme as a theory which can be developped succesfully in different contexts. It was useful to describe some mechanical systems, the so called generalized Toda, and now it…
We present a slight generalization of the notion of completely integrable systems to get them being integrable by quadratures. We use this generalization to integrate dynamical systems on double Lie groups.
We show how to construct 2d field theories with holomorphic integrability from defect setups in 4d holomorphic BF. In a simple example setup, we explicitly construct the 2d theory and perform an initial classical analysis. Making use of the…
We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.
In this paper we give an overview of results on the analysis of parametric linear hybrid automata, and of systems of similar linear hybrid automata: We present possibilities of describing systems with a parametric (i.e. not explicitly…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
In recent years, significant progress has been made in the study of integrable systems from a gauge theoretic perspective. This development originated with the introduction of $4$d Chern-Simons theory with defects, which provided a…
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular…
The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand…
Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant…
This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of…
The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
In this article we consider integrable systems on manifolds endowed with singular symplectic structures of order one. These structures are symplectic away from an hypersurface where the symplectic volume goes either to infinity or to zero…
We study the pseudo-Hermitian systems with general spin-coupling point interactions and give a systematic description of the corresponding boundary conditions for PT-symmetric systems. The corresponding integrability for both bosonic and…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…