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The nonlinear Schrodinger equation with t-periodic data: I. Exact 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, 20140925Article in journal (Refereed) Published
Abstract [en]

We consider the nonlinear Schrodinger equation on the half-line with a given Dirichlet (Neumann) boundary datum which for large t tends to the periodic function g(0)(b)(t) (g(1)(b)(t)). Assuming that the unknown Neumann (Dirichlet) boundary value tends for large t to a periodic function g(1)(b)(t) (g(0)(b)(t)), we derive an easily verifiable condition that the functions g(1)(b)(t) and g(0)(b)(t) must satisfy. Furthermore, we propose two different methods, one based on the formulation of a Riemann-Hilbert problem and the other based on a perturbative approach, for constructing g(1)(b)(t) (g(0)(b)(t)) in terms of g(0)(b)(t) (g(1)(b)(t)).

Place, publisher, year, edition, pages
ROYAL SOC , 2015. Vol. 471, no 2181, 20140925
Keyword [en]
Macrodispersion, Solute Transport, Tracer Tests, Groundwater, Scale Effect, Unique Scaling Law
National Category
Mathematical Analysis
URN: urn:nbn:se:kth:diva-176983DOI: 10.1098/rspa.2014.0925ISI: 000363482200001ScopusID: 2-s2.0-84943163535OAI: diva2:872240

QC 20151118

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

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Lenells, Jonatan
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