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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 122, Number 1, Pages 128–143
DOI: https://doi.org/10.4213/tmf560
(Mi tmf560)
 

Initial boundary value problems for the nonlinear Schrödinger equation

B. Pelloni

Imperial College, Department of Mathematics
References:
Abstract: A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrцdinger equation and to its linearized version in the domain $\{x\geq l(t),t\geq0\}$. We show that there exist two cases: a) if $l''(t)<0$, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann–Hilbert problem, which is defined on a time-dependent contour; b) if $l''(t)>0$, then the Riemann–Hilbert problem is replaced by a respective scalar or matrix $\overline\partial$ problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.
English version:
Theoretical and Mathematical Physics, 2000, Volume 122, Issue 1, Pages 107–120
DOI: https://doi.org/10.1007/BF02551174
Bibliographic databases:
Language: Russian
Citation: B. Pelloni, “Initial boundary value problems for the nonlinear Schrödinger equation”, TMF, 122:1 (2000), 128–143; Theoret. and Math. Phys., 122:1 (2000), 107–120
Citation in format AMSBIB
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\by B.~Pelloni
\paper Initial boundary value problems for the nonlinear Schr\"odinger equation
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\yr 2000
\vol 122
\issue 1
\pages 128--143
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\crossref{https://doi.org/10.4213/tmf560}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1776512}
\zmath{https://zbmath.org/?q=an:0957.35119}
\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 122
\issue 1
\pages 107--120
\crossref{https://doi.org/10.1007/BF02551174}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000086224200011}
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  • https://doi.org/10.4213/tmf560
  • https://www.mathnet.ru/eng/tmf/v122/i1/p128
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:57
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