Abstract This work proposes a new parameter identification method based on the Wentzel-Kramers-Brillouin (WKB) approximation for slow linear time-varying (LTV) dynamic systems. The considered time period is divided into series of short windows. In each window, assumption “short linearly varying” parameters employed, and nonlinear optimization problem solved using WKB results LTV system. A searc...

Abstract. We give a unified approach to the Krall-type polynomials orthogonal with respect to a positive measure consisting of an absolutely continuous one ‘perturbed’ by the addition of one or more Dirac delta functions. Some examples studied by different authors are considered from a unique point of view. Also some properties of the Krall-type polynomials are studied. The threeterm recurrence...

The turning point problems for instanton-type solutions of Painlevé equations with a large parameter are discussed. Generalizing the main result of [KT2] near a simple turning point, we report in this paper that Painlevé equations can be transformed to the second Painlevé equation and the most degenerate third Painlevé equation near a double turning point and near a simple pole, respectively. A...

We illustrate the physical significance and mathematical origin of resurgent trans-series expansions for energy eigenvalues in quantum mechanical problems with degenerate harmonic minima, by using the uniform WKB approach. We provide evidence that the perturbative expansion, combined with a global eigenvalue condition, contains all information needed to generate all orders of the non-perturbati...

Demographic noise causes unlimited population growth in a broad class of models which, without noise, would predict a stable finite population. We study this effect on the example of a stochastic birth-death model which includes immigration, binary reproduction and death. The unlimited population growth proceeds as an exponentially slow decay of a metastable probability distribution (MPD) of th...

In this paper, we consider the spectral stability of spatially periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long-wavelength perturbations. Specifically, we extend the work of Bronski and Johnson by demonstrating that the homogenized system describing the mean behavior of a slow modulation (WKB) approximation of the solution correctly describes the linearize...