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Asymptotic Analysis - Volume 48, issue 4

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Price: EUR 420.00
ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2024: 1.1

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. 

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

Liouville–Green asymptotics for almost-diagonal second-order matrix differential equations

Authors: Spigler, Renato | Vianello, Marco

Article Type: Research Article

Abstract: A WKB (or Liouville–Green) asymptotic approximation theory is developed for the class of linear second-order matrix differential equations Y″=(D(t)+G(t))Y, on [a,+∞), where D(t) is a nonsingular diagonal matrix. A basis for the right-module of its solutions can be represented explicitly, and precise computable bounds for the error terms involved are given. The double asymptotic nature with respect to both, t and some parameters that might affect the matrix coefficient, is shown. Examples and applications are given.

Keywords: Liouville–Green asymptotics, WKB approximation, almost-diagonal systems of ordinary differential equations, generalized Airy functions

Citation: Asymptotic Analysis, vol. 48, no. 4, pp. 267-294, 2006

Price: EUR 27.50

On the eigenvalues for slowly varying perturbations of a periodic Schrödinger operator

Authors: Marx, Magali

Article Type: Research Article

Abstract: In this paper, I consider one-dimensional periodic Schrödinger operators perturbed by a slowly decaying potential. In the adiabatic limit, I give an asymptotic expansion of the eigenvalues in the gaps of the periodic operator. When one slides the perturbation along the periodic potential, these eigenvalues oscillate. I compute the exponentially small amplitude of the oscillations.

Keywords: eigenvalues, complex WKB method, scattering, adiabatic perturbations

Citation: Asymptotic Analysis, vol. 48, no. 4, pp. 295-357, 2006

Price: EUR 27.50

Author Index Volume 48 (2006)

Article Type: Other

Citation: Asymptotic Analysis, vol. 48, no. 4, pp. 359-360, 2006

Price: EUR 27.50
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