相关论文: Theory of Newtonian self-gravitating stationary sp…

We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced…

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…

We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a simple criterion, we prove the nonlinear stability of steady states which are decreasing functions…

We study an effective quantum description of the static gravitational potential for spherically symmetric systems up to the first post-Newtonian order. We start by obtaining a Lagrangian for the gravitational potential coupled to a static…

We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the…

In this paper, we study the dynamic of position-dependent mass system confined in harmonic oscillator potential. We derive the eigensystems by solving the Schr\''odinger-like equation which describes this system. We construct coherent…

We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…

Using the Newtonian approximation, we study rotating compact bosonic objects. The equations which describe stationary states with non-zero angular momentum are constructed and some numerical results are presented as examples. Limits on the…

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider $f(R)=R+{\epsilon}R^2$ model and assume hydrostatic equilibrium of the axial…

We study static spherically-symmetric solutions of non-Abelian gauge theory coupled to Conformal Gravity. We find solutions for the self-gravitating pure Yang-Mills case as well as monopole-like solutions of the Higgs system. The former are…

We investigate discret conditions for stability and asymptotic stability by Lyapunov and the point of equilibrium of autonomous system of differential equations.

The results on local existence and continuation criteria obtained by G. Rein in [4] are extended to the case with a non-zero cosmological constant. It is also shown that for the spherically symmetric case and a positive cosmological…

The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…

We present a new self-consistent perturbative expansion for realistic isolated differentially rotating systems -- disc galaxies. At leading order it is formally equivalent to Ehlers' Newton-Cartan limit, which we reinterpret in terms of…

We consider the Schr\"odinger--Poisson system on the complete, simply-connected Riemannian manifolds of constant sectional curvature. We obtain closed-form stationary spherically-symmetric solutions for the homogeneous equations for certain…

We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for…

We study the ground state and the first three radially excited states of a self-gravitating Bose-Einstein- Condensate with respect to the influence of two external parameters, the total mass and the strength of interactions between…

This article is a review of results on the nonlinear Schroedinger / Gross-Pitaevskii equation (NLS / GP). Nonlinear bound states and aspects of their stability theory are discussed from variational and bifurcation perspectives. Nonlinear…

The Nordstr\"om-Vlasov system describes the dynamics of a self-gravitating ensemble of collisionless particles in the framework of the Nordstr\"om scalar theory of gravitation. We prove existence and uniqueness of classical solutions of the…

Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing…