Change search
ReferencesLink to record
Permanent link

Direct link
The nonlinear Schrodinger equation with t-periodic data: II. Perturbative results
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6191-7769
2015 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 471, no 2181, 20140926Article in journal (Refereed) Published
Abstract [en]

We consider the nonlinear Schrodinger equation on the half-line with a given Dirichlet boundary datum which for large t tends to a periodic function. We assume that this function is sufficiently small, namely that it can be expressed in the form alpha g(0)(b)(t), where alpha is a small constant. Assuming that the Neumann boundary value tends for large t to the periodic function g(1)(b)(t), we show that g(1)(b)(t) can be expressed in terms of a perturbation series in alpha which can be constructed explicitly to any desired order. As an illustration, we compute g(1)(b)(t) to order alpha(8) for the particular case that g(0)(b)(t) is the sum of two exponentials. We also show that there exist particular functions g(0)(b)(t) for which the above series can be summed up, and therefore, for these functions, g(1)(b)(t) can be obtained in closed form. The simplest such function is exp(i omega t), where omega is a real constant.

Place, publisher, year, edition, pages
Royal Soc , 2015. Vol. 471, no 2181, 20140926
Keyword [en]
Initial-Boundary Value Problem, Time-Periodic Data, Long-Time Asymptotics
National Category
Mathematical Analysis
URN: urn:nbn:se:kth:diva-176982DOI: 10.1098/rspa.2014.0926ISI: 000363482200002ScopusID: 2-s2.0-84943179325OAI: diva2:872253

QC 20151118

Available from: 2015-11-18 Created: 2015-11-13 Last updated: 2015-11-18Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Lenells, Jonatan
By organisation
Mathematics (Div.)
In the same journal
Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 22 hits
ReferencesLink to record
Permanent link

Direct link