Related papers: Point vortices on the hyperbolic plane
The motion of a pair of counter-rotating point vortices placed in a uniform flow around a circular cylinder forms a rich nonlinear system that is often used to model vortex shedding. The phase portrait of the Hamiltonian governing the…
This paper shows nonlinear stability of homogeneous states in second-order hyperbolic systems of partial differential equations that model the dynamics of dissipative relativistic fluids, by checking a dissipativity criterion formulated…
Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schr\"{o}dinger equation. The existence and stability of vortex…
We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and the derivation of a delicate estimate on the relative…
We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's…
We examine existence and stability of relative equilibria of the $n$-vortex problem specialized to the case where $N$ vortices have small and equal circulation and one vortex has large circulation. As the small circulation tends to zero,…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases
In this paper, we have obtained motion equations for a wide class of one-dimensional singularities in 2-D ideal hydrodynamics. The simplest of them, are well known as point vortices. More complicated singularities correspond to vorticity…
There is a lack of knowledge about the topological invariants of non-linear $d$-dimensional systems with a periodic potential. We study these systems through a classification of the linearized NLS/GP equation around their soliton solutions.…
The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium…
We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class which we call normal, and a non-generic abnormal class. The…
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…
In this paper, we investigate some dynamical properties near a nonhyperbolic fixed point. Under some conditions on the higher nonlinear terms, we establish a stable manifold theorem and a degenerate Hartman theorem. Furthermore, the finite…
We present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically…
A general exact weak solution to the nonlinear equation of the conservation of the absolute vorticity in a thin layer of an incompressible medium on a rotating sphere is proposed. It takes into account the helicity of the point vortices and…
A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group…
We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further…
Irrotational relativistic vortex configurations in uniform subsonic motion with respect to a surrounding perfect fluid are analysed for the purpose of application to superfluid layers in neutron stars. Asymptotic solutions are found by…
Super-Bloch oscillations are the outcome of a relative phase between Bloch oscillations and modulations of the periodic lattice. We analyze the dynamics for a model system in which such a relative phase is intrinsically present due to the…