The nonlinear Schrodinger equation with t-periodic data: II. Perturbative results
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
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
Initial-Boundary Value Problem, Time-Periodic Data, Long-Time Asymptotics
IdentifiersURN: urn:nbn:se:kth:diva-176982DOI: 10.1098/rspa.2014.0926ISI: 000363482200002ScopusID: 2-s2.0-84943179325OAI: oai:DiVA.org:kth-176982DiVA: diva2:872253
QC 201511182015-11-182015-11-132015-11-18Bibliographically approved