Related papers: Point vortices on the hyperbolic plane

A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…

This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before…

We study the stability and bifurcation of relative equilibria of a particle on the Lie group $SO(3)$ whose motion is governed by an $SO(3)\times SO(2)$ invariant metric and an $SO(2)\times SO(2)$ invariant potential. Our method is to reduce…

We determine the modulational stability of standing waves with small group velocity in quasi-onedimensional systems slightly above the threshold of a supercritical Hopf bifurcation. The stability limits are given by two different…

We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic Riemannian data of the problem.

Homoclinic chaos is usually examined with the hypothesis of hyperbolicity of the critical point. We consider here, following a (suitably adjusted) classical analytic method, the case of non-hyperbolic points and show that, under a…

In the article we study a hyperbolic-elliptic system of PDE. The system can describe two different physical phenomena: 1st one is the motion of magnetic vortices in the II-type superconductor and 2nd one \ is the collective motion of cells.…

Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold…

The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions…

Equilibrium solutions are believed to structure the pathways for ergodic trajectories in a dynamical system. However, equilibria are atypical for systems with continuous symmetries, i.e. for systems with homogeneous spatial dimensions,…

This paper extends the model reduction method by the operator projection to the three-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order moment system is built on our careful study of infinite families of…

With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with…

It has been observed empirically that two dimensional vortices tend to cluster forming a giant vortex. To account for this observation Onsager introduced a concept of negative absolute temperature in equilibrium statistical mechanics. In…

Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition…

We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose-Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a…

This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be…

We report the existence of hydrostatic equilibrium states for a composite body made of two rigidly rotating, homogeneous layers bounded by spheroidal surfaces, where the core has a prolate shape. These new configurations require an oblate…

This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison…

We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response…