Related papers: Implications of nonlinearity for spherically symme…
A solution of the linearized Einstein's equations for a spherically symmetric perturbation of the ultrarelativistic fluid in the homogeneous and isotropic universe is obtained. Conditions on the boundary of the perturbation are discussed.…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
We compute the tensorial perturbations to a general spherically symmetric metric in d dimensions with string-theoretical corrections quadratic in the Riemann tensor, from which we derive their respective potential. We use this result to…
We study the evolution of nonlinear superhorizon perturbations in a universe dominated by a complex scalar field. The analysis is performed adopting the gradient expansion approach, in the constant mean curvature slicing. We derive general…
We prove the non-linear stability of a large class of spherically symmetric equilibrium solutions of both the collisonless Boltzmann equation and of the Euler equations in MOND. This is the first such stability result that is proven with…
We study the quasi-periodic oscillations from the accretion disk around the distorted Schwarzschild black hole in the framework of the resonant models. We confine ourselves to the case of a quadrupole distortion which can be caused for…
We investigate black hole solutions with time-dependent (scalar) hair in scalar-tensor theories. Known exact solutions exist for such theories at the background level, where the metric takes on a standard GR form (e.g. Schwarzschild-de…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
We perform dynamical and nonlinear numerical simulations to study critical phenomena in the gravitational collapse of massless scalar fields in the absence of spherical symmetry. We evolve axisymmetric sets of initial data and examine the…
Two-dimensional (axially symmetric) numerical hydrodynamical calculations of accretion flows which cannot cool through emission of radiation are presented. The calculations begin from an equilibrium configuration consisting of a thick torus…
The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…
In this letter we review the separate universe approach for cosmological perturbations and point out that it is essentially the lowest order approximation to a gradient expansion. Using this approach, one can study the nonlinear evolution…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
In this work, we discuss the accretion onto static spherical symmetric regular black holes for specific choices of equation of state parameter. The underlying regular black holes are charged regular black hole using Fermi-Dirac…
Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such systems which appears…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…