In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

In this paper we present conditions for the preservation of strong and polynomial stability of a strongly continuous semigroup under unbounded finite rank perturbations of its infinitesimal generator. In addition, we also improve recent perturbation results for bounded finite rank perturbations. The results are illustrated with two examples. In the first one we consider the preservation of stab...

We study the 2D vortex-free XY model in a random field, a model for randomly pinned flux lines in a plane. We construct controlled RG recursion relations which allow for replica symmetry breaking (RSB). The fixed point previously found by Cardy and Ostlund in the glass phase T < Tc is unstable to RSB. The susceptibility χ associated to infinitesimal RSB perturbation in the high-temperature phas...

Comparison of oscillatory behaviors of a gravitating infinite Nambu-Goto string with a test string is discussed using the general relativistic gauge invariant perturbation technique with two infinitesimal parameters on the flat spacetime background. Due to the existence of the pp-wave exact solution, we see that the conclusion “dynamical degree of freedom of an infinite Nambu-Goto string is com...

This article provides our perspective on the problem of active control of combustion instability. It makes no claim to complete or historically accurate survey, but attempts to put our past work in the context of existing literature. Starting with an equation for the energy of a general type of infinitesimal disturbance, we argue that the perturbation energy can be mitigated (or enhanced) by su...

Stochastic Flow Models (SFMs) form a class of hybrid systems used as abstractions of complex Discrete Event Systems (DES) for the purpose of deriving performance sensitivity estimates through Infinitesimal Perturbation Analysis (IPA) techniques when these cannot be applied to the original DES. In this paper, we establish explicit connections between gradient estimators obtained through a SFM an...

We investigate the nontrivial characteristics of modulational instability (MI) in a system Bragg gratings with saturable nonlinearity. also introduce an equal amount gain and loss into existing system, which gives rise to additional degree freedom, due concept $\mathcal{PT}$ symmetry. obtain nonlinear dispersion relation model discover that such relations for both conventional $\mathcal{PT}$-sy...

We consider expected performances based on max-stable random fields and we are interested in their derivatives with respect to the spatial dependence parameters of those fields. Max-stable fields, such as Brown–Resnick Smith very popular extremes. focus two most unbiased stochastic derivative estimation approaches: likelihood ratio method (LRM) infinitesimal perturbation analysis (IPA). LRM req...

The dynamical behaviour of the forced escape oscillator, which depends on the parameter values we considered, have been studied numerically using the techniques of phase portraits and Poincar'{e} sections. Also, we employed perturbation methods such as Lindstedt's method to obtain the frequency-amplitude relation of escape oscillator.