Abstract-Several types of waves in a layered composite material were examined. In order to obtain explicit approximate solutions. a perturbation method was used. This approach views the nonhomogeneous layering as a perturbation on a homogeneous but anisotropic solid. For propagation normal to the direction of layering, it was necessary to include the second-order perturbation terms to get quali...

We explore via linearized perturbation theory the Gregory-Laflamme instability of the black string solutions of Einstein’s equations with negative cosmological constant recently discussed in literature. Our results indicate that the black strings whose conformal infinity is the product of time and S × S are stable for large enough values of the event horizon radius. All topological black string...

It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations which are usually derived by the reductive perturbation theory are shown to be naturally derived as the equations describing the envelopes of the local solution...

We construct two solutions of the minimally coupled Einstein–scalar field equations, representing regular deformations of Schwarzschild black holes by a selfinteracting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theor...

We investigate the asymptotic behavior at time infinity of solutions close to a nonzero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau-Schrödinger) equation. We prove that, in dimensions larger than 3, small perturbations can be approximated at time infinity by the linearized evolution, and the wave operators are homeomorphic around 0 in certain Sobolev spaces.

In this paper we prove existence of multiple-front solutions in a class of coupled reaction-diiusion equations with a small parameter. By a travelling wave Ansatz we reduce the problem to a four-dimensional system of ordinary diierential equations and prove existence of a large variety of n-jump homoclinic and heteroclinic solutions, n = 1; 2; 3; : : : using geometric singular perturbation theo...

Inhibition in oscillatory networks of neurons can have apparently paradoxical e ects, sometimes creating dispersion of phases, sometimes fostering synchrony in the network. We analyze a pair of biophysically modeled neurons and show how the rates of onset and decay of inhibition interact with the time scales of the intrinsic oscillators to determine when stable synchrony is possible. We show th...

The Lagrangian perturbation theory on Friedmann– Lemaı̂tre cosmologies is compared with numerical simulations (tree–, adaptive P3M– and PM codes). In previous work we have probed the large–scale performance of the Lagrangian perturbation solutions up to the third order by studying their cross–correlations with N–body simulations for various power spectra (Buchert et al. 1994, Melott et al. 1995,...

General solution of RG equations in the framework of background perturbation theory is written down in the large Nc limit. A simplified (model) approximation to the general solution is suggested which allows to write β(α) and α(β) to any loop order. The resulting αB(Q 2) coincides asymptotically at large |Q2| with standard (free) αs, saturates at small Q2 ≥ 0 and has poles at time-like Q2 in ag...

We study a scalar field in curved space in three dimensions. We compare the results obtained by using perturbation theory and numerical solutions, especially regarding to singularity behaviour at infinity. We find that both methods point to the necessity of excising the space-time around the origin. key words: black holes, Choptuik formation, + [email protected] * [email protected]