相关论文: Non-linear stability in photogravitational non-pla…

The classical model of a star is the Lane-Emden star with dynamics governed by the Euler-Poisson equations. We consider the case of a liquid star with a "stiffened gas" equation of state $p=\rho^\gamma-1$. We derive the full 3D linearised…

We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…

We consider linearly stable elliptic fixed points for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. Morbidelli and Giorgilli have proved a theorem of stability over…

We construct a Nekhoroshev-like result of stability with sharp constants for the planar three body problem, both in the planetary and in the restricted circular case, by using the periodic averaging technique. Our constructions can be…

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 demonstrate experimentally that in a centrosymmetric paraelectric non-stationary boundary conditions can dynamically halt the intrinsic instability of quasi-steady-state photorefractive self-trapping, driving beam evolution into a stable…

This paper addresses the existence and spectral stability of traveling fronts for nonlinear hyperbolic equations with a positive "damping" term and a reaction function of bistable type. Particular cases of the former include the relaxed…

Continuing work initiated in an earlier publication [H. Asada, Phys. Rev. D {\bf 80}, 064021 (2009)], the gravitational radiation reaction to Lagrange's equilateral triangular solution of the three-body problem is investigated in an…

In this paper, we consider the elliptic relative equilibria of the restricted $4$-body problems, where the three primaries form an Euler collinear configuration and the four bodies span $\mathbf{R}^2$. We obtain the symplectic reduction to…

Let (M,g) be a compact Riemmanian manifold with non-empty boundary. Consider the second order hyperbolic initial-boundary value problem (\delta_t^2 + P(x,D))u = 0 in (0,T) x M, u(0,x) = \delta_t u(0,x) = 0 for x in M, u(t,x) = f(t,x) on…

?In this work, we study the orbital stability of stationary solutions to the relativistic Vlasov-Manev system. This system is a kinetic model describing the evolution of a stellar system subject to its own gravity with some relativistic…

Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different…

We investigate the stability and stabilization of the cubic focusing Klein-Gordon equation around static solutions on the closed ball of radius L in $\mathbb{R}^3$. First we show that the system is linearly unstable near the static solution…

In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. Two examples of normalization in the…

In this paper, we consider the elliptic relative equilibria of the restricted $N$-body problems, where the $N-1$ primaries form an Euler-Moulton collinear central configuration or a $(1+n)$-gon central configuration. We obtain the…

This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits…

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…

Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…

We prove the orbital stability of soliton solutions for 2D Maxwell--Lorentz system with extended charged particle. The solitons corresponds to the uniform motion and rotation of the particle. We reduce the corresponding Hamilton system by…

A simplified model of the tumor angiogenesis can be described by a Keller-Segel equation \cite{FrTe,Le,Pe}. The stability of traveling waves for the one dimensional system has recently been known by \cite{JinLiWa,LiWa}. In this paper we…