Related papers: Stability of Hamiltonian relative equilibria in sy…
In this paper we provide sharp criteria for linear stability or instability of equilibria of collisionless plasmas in the presence of boundaries. Specifically, we consider the relativistic Vlasov-Maxwell system with specular reflection at…
Orbital and asymptotic stability for 1-soliton solutions to the Toda lattice equations as well as small solitary waves to the FPU lattice equations are established in the energy space. Unlike analogous Hamiltonian PDEs, the lattice…
In this note we study contractivity of monotone systems and exponential convergence of positive systems using non-Euclidean norms. We first introduce the notion of conic matrix measure as a framework to study stability of monotone and…
In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling 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 performed a pump-probe experiment on the chiral magnet Cu$_2$OSeO$_3$ to study the relaxation dynamics of its non-collinear magnetic orders, employing a millisecond magnetic field pulse as the pump and resonant elastic x-ray scattering…
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…
In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations and in particular at the relative strengths of the toroidal and poloidal components. Both toroidal and…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
The first result in this study is a non-existence theorem for $\alpha-$harmonic mappings. Additionally, a direct connection between the $\alpha-$ harmonic and harmonic maps is made possible via conformal deformation. Second, the instability…
We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also…
Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of…
We establish the asymptotic stability of multi-solitons for the one-dimensional Landau-Lifshitz equation with an easy-plane anisotropy. The solitons have non-zero speed, are ordered according to their speeds and have sufficiently separated…
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…
We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of…
This paper presents elements about the radial orbit instability, which occurs in spherical self-gravitating systems with a strong anisotropy in the radial velocity direction. It contains an overview on the history of radial orbit…
We investigate the global nonaxisymmetric Rossby vortex instability in a differentially rotating, compressible magnetized accretion disk with radial density structures. Equilibrium magnetic fields are assumed to have only the toroidal…
For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
The (group and spin space) matrix Hamiltonian describing the dynamics of a nonrelativistic spin 1/2 particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an…