Related papers: The Integration Algorithm for Nilpotent Orbits of …

In the present work, we study Hamiltonian systems on (co)adjoint orbits and propose a Lax pair formalism for Gelfand-Tsetlin integrable systems defined on (co)adjoint orbits of the compact Lie groups ${\rm{U}}(n)$ and ${\rm{SO}}(n)$. In the…

We establish the Liouville integrability of the differential equation $\dot S(t)= [N,S^2(t)],$ recently considered by Bloch and Iserles. Here, $N$ is a real, fixed, skew-symmetric matrix and $S$ is real symmetric. The equation is realized…

The geodesics of the rotating extreme black hole in five spacetime dimensions found by Breckenridge, Myers, Peet and Vafa are Liouville integrable and may be integrated by additively separating the Hamilton-Jacobi equation. This allows us…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

Here we present an efficient method for finding and using a nonlocal symmetry admitted by a rational second order ordinary differential equation (rational 2ODE) in order to find a Liouvillian first integral (belonging to a vast class of…

The integrability of the classical and quantum rational Calogero-Moser systems is verified explicitly via the Lax pair method for the case $n=3$. We provide an extensive survey of reflection groups and root systems. The…

The explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic…

We explore the integrability of five-dimensional minimal supergravity in the presence of three commuting Killing vectors. We argue that to see the integrability structure of the theory one necessarily has to perform an Ehlers reduction to…

Let $G$ be a reductive group, and let $X$ be a smooth quasi-projective complex variety. We prove that any $G$-irreducible, $G$-cohomologically rigid local system on $X$ with finite order abelianization and quasi-unipotent local monodromies…

The aim of this paper is to prove the existence of periodic solutions to symmetric Newtonian systems in any neighborhood of an isolated orbit of equilibria. Applying equivariant bifurcation techniques we obtain a generalization of the…

We prove that any bi-Hamiltonian system $v = \left(\mathcal{A} + \lambda \mathcal{B}\right)dH_{\lambda}$ on a real smooth manifold that is Hamiltonian with respect all Poisson brackets $\left(\mathcal{A} + \lambda \mathcal{B}\right)$ is…

The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…

Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…

We present a detailed analysis of the behavior of the triaxial Schwarzschild orbit superposition method near the axisymmetric limit. Orbit superposition modeling is the primary method used to determine dynamical masses of supermassive black…

We review the remarkable progress that has been made the last 15 years towards the classification of supersymmetric solutions with emphasis on the description of the bilinears and spinorial geometry methods. We describe in detail the…

Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded…

We classify states of four rebits, that is, we classify the orbits of the group $\widehat{G}(\mathbb R) = \mathrm{\mathop{SL}}(2,\mathbb R)^4$ in the space $(\mathbb R^2)^{\otimes 4}$. This is the real analogon of the well-known SLOCC…

The present article is concerned with the s*-compressibility of classical boundary integral operators in anisotropic wavelet coordinates. Having the s*-compressibility at hand, one can design adaptive wavelet algorithms which are…

We argue that one of the basic ingredients for the appearance of soliton solutions in integrable hierarchies, is the existence of ``vacuum solutions'' corresponding to Lax operators lying in some abelian subalgebra of the associated affine…

Four dimensional N=2 supergravity has regular, stationary, asymptotically flat BPS solutions with intrinsic angular momentum, describing bound states of separate extremal black holes with mutually nonlocal charges. Though the existence and…