We investigate the stability of a family of spherically symmetric static solutions in vacuum Brans-Dicke theory ~with v50) recently described by van Putten. Using linear perturbation theory, we find one exponentially growing mode for every member of the family of solutions, and thus conclude that the solutions are not stable. Using a previously constructed code for spherically symmetric Brans-D...

Abstract. Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action variables. We show that the renormalization group method gives the same approximate solutions as canonical perturbation theory up to the second order of...

We study the behavior of gravitational waves and their backreaction on the background in cosmological solutions of the five-dimensional Hořava-Witten theory. As a dynamical background, we consider two cosmological solutions with spatially flat expanding FRW branes, called (↑)and (↓)-solutions, in which the orbifold size increases and decreases in time, respectively. For these background solutio...

We consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the perturbation. We assume that the unperturbed system is locally integrable and anisochronous, and that the frequency vector of the perturbation satisfies the Bryuno condi...

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. The examples of particlelike and wave-like solutions are given.

In this article, the homotopy perturbation method is proposed to solve systems of Volterra integral equations of the first kind. Theoretical proposes are presented briefly, so that this paper can be read independently. To illustrate the method some examples are presented. The results reveal that the homotopy perturbation method is very effective and simple and gives the exact solutions.

In ordinary differential equations of singular perturbation type, the dynamics of solutions near saddle-node bifurcations of equilibria are rich. Canard solutions can arise, which, after spending time near an attracting equilibrium, stay near a repelling branch of equilibria for long intervals of time before finally returning to a neighborhood of the attracting equilibrium (or of another attrac...

In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic. the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent ca...

We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R.

[1] In this paper we derive analytical solutions to statistical moments for transient saturated flow in two-dimensional, bounded, randomly heterogeneous porous media. By perturbation expansions, we first derive partial differential equations governing the zerothorder head h and the first-order head term h, where orders are in terms of the standard deviation of the log transmissivity. We then so...