Interface problems for dispersive equations

Natalie E. Sheils, Bernard Deconinck

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

The interface problem for the linear Schrödinger equations in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the wave function and a jump in their derivative at the interface are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. The problem and the method considered here extend that of an earlier paper by Deconinck et al. (2014) [1]. The dispersive nature of the problem presents additional difficulties that are addressed here.

Original languageEnglish (US)
Pages (from-to)253-275
Number of pages23
JournalStudies in Applied Mathematics
Volume134
Issue number3
DOIs
StatePublished - Apr 1 2015

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