Related papers: Charting the AdS Islands of Stability with Multi-o…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition…
We consider existence and stability properties of nonlinear spatially periodic or quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic oscillators. Specifically, we consider Klein-Gordon (KG) chains with…
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -…
Coupled distinct arrays of nonlinear oscillators have been shown to have a regime of high frequency, or ultra-harmonic, oscillations that are at multiples of the natural frequency of individual oscillators. The coupled array architectures…
We discuss two types of instabilities which may arise in string theory compactified to asymptotically AdS spaces: perturbative, due to discrete modes in the spectrum of the Laplacian, and non-perturbative, due to brane nucleation. In the…
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…
Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Li\'enard type oscillators exhibit this interesting property. We show that a…
We consider the linearized instability of 2D irrotational solitary water waves. The maxima of energy and the travel speed of solitary waves are not obtained at the highest wave, which has a 120 degree angle at the crest. Under the…
This paper studies the stability and large-time behavior of the three-dimensional (3-D) Boltzmann equation near shock profiles. We prove the nonlinear stability of the composite wave consisting of two shock profiles under general…
We investigate the existence of dS vacua in supersymmetry-breaking Scherk-Schwarz toroidal compactifications of type II string theory, using the well-understood ingredients of curvature, fluxes and 1-loop Casimir energy. Starting from the…
We present a construction of a perturbatively stable non-supersymmetric type II closed string model in four dimensions. It is based on a freely acting Scherk-Schwarz Z2-deformation of a supersymmetric construction which is recovered in…
The stability properties of a family of magnetic $AdS_{3}\times \mathbb{R}^{2}$ solutions of D=5, SO(6) gauged SUGRA are investigated in more detail. We construct an analogous family of magnetic $AdS_{2}\times \mathbb{R}^{2}$ solutions of…
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
We study the dynamics of a spherically symmetric thin shell of perfect fluid embedded in d-dimensional Anti-de Sitter space-time. In global coordinates, besides collapsing solutions, oscillating solutions are found where the shell bounces…
The stability of certain class of asymptotically AdS wormholes in vacuum against scalar field perturbations is analyzed. For a free massive scalar field, the stability of the perturbation is guaranteed provided the squared mass is bounded…
We investigate the existence and the stability of spherically symmetric thermal equilibrium states of the self-gravitating many-particle system which satisfies the Einstein-Vlasov equations with a negative cosmological constant. While a…