Related papers: What drives AdS unstable?
We study the existence and stability of the standing waves for the periodic cubic nonlinear Schr\"odinger equation with a point defect determined by a periodic Dirac distribution at the origin. This equation admits a smooth curve of…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude epsilon on time-scales of order…
We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the…
A large class of multidimensional nonlinear Schroedinger equations admit localized nonradial standing wave solutions that carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are…
Approximating nonlinear dynamics with a truncated perturbative expan- sion may be accurate for a while, but it in general breaks down at a long time scale that is one over the small expansion parameter. There are interesting occasions in…
We study the stability of anti-de Sitter (AdS) spacetime to spherically symmetric perturbations of a real scalar field in general relativity. Further, we work within the context of the "two time framework" (TTF) approximation, which…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
Stable non-supersymmetric Anti-de Sitter (AdS) vacua of string theory are widely believed not to exist. In this letter, we analytically compute the full bosonic Kaluza-Klein spectrum around the ${\rm G_2}$-invariant non-supersymmetric…
Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that…
We study the steady uniphase and multiphase solutions of the discretized nonlinear damped wave equation.Conditions for the stability abd instability of the steady solutions are given;in the instability case the linear stable and unstable…
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical…
Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp $L^p$ estimates on the linearized solution operator about a multidimensional planar periodic…
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…
This paper investigates the nature of the MHD turbulence excited by the streaming of accelerated cosmic rays in a shock wave precursor. The two recognised regimes (non-resonant and resonant) of the streaming instability are taken into…
We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…
Rotating small AdS black holes exhibit the superradiant instability to low-frequency scalar perturbations, which is amenable to a complete analytic description in four dimensions. In this paper, we extend this description to all higher…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The thermomagnetic instability of the critical state in superconductors is analysed with account of the dissipation and dispersion. The possibility is demonstrated of the existance of a nonlinear shok wave describing the final stage of the…