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Averaging for some periodic and random nonlinear Schrödinger models

✍ Scribed by J. Feng; P.G. Kevrekidis

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
332 KB
Volume
74
Category
Article
ISSN
0378-4754

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✦ Synopsis

In the present communication, we derive averaging equations for nonlinear Schrödinger settings with periodic as well as ergodic random potentials. Our case examples are motivated by recent experimentally accessible applications in soft-condensed matter, as well as in optical physics. Particular features of the resulting equations are compared directly with corresponding predictions of the original model and good agreement is found between the two. Higher order corrections to the leading order averaging results are also discussed. Published by Elsevier B.V. on behalf of IMACS.

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✍ Minbo Yang 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 476 KB

In this paper we consider the following Schrödinger equation: where V is a periodic continuous real function with 0 in a gap of the spectrum σ (A), A := -∆ + V and the classical Ambrosetti-Rabinowitz superlinear condition on g is replaced by a general super-quadratic condition.