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Izvestiya: Mathematics, 1997, Volume 61, Issue 4, Pages 757–794
DOI: https://doi.org/10.1070/im1997v061n04ABEH000137
(Mi im137)
 

This article is cited in 9 scientific papers (total in 9 papers)

Solution asymptotics at large times for the non-linear Schrödinger equation

P. I. Naumkin

M. V. Lomonosov Moscow State University
References:
Abstract: We consider a spatially uniform asymptotic representation at large times of the solution to the Cauchy problem for the non-linear Schrödinger equation. If the non-linear term decreases in time faster than the linear terms, then the asymptotics are quasi-linear. Of particular interest is the case in which the non-linearity decreases in time at the same rate as or even more slowly then the linear terms and thus has a stronger effect on the solution asymptotics at large times. In this paper we employ an appropriate change of variables to reduce this case to the quasi-linear one. Namely, we derive an integral equation with rapidly decreasing non-linearity for the new unknown function, which can be solved by the method of successive approximations. Thus, we have a constructive algorithm for calculating the asymptotics of the solution to the Cauchy problem for the non-linear Schrödinger equation from the initial data.
Received: 12.09.1995
Bibliographic databases:
MSC: 35Q55, 58F07
Language: English
Original paper language: Russian
Citation: P. I. Naumkin, “Solution asymptotics at large times for the non-linear Schrödinger equation”, Izv. Math., 61:4 (1997), 757–794
Citation in format AMSBIB
\Bibitem{Nau97}
\by P.~I.~Naumkin
\paper Solution asymptotics at large times for the non-linear Schr\"odinger equation
\jour Izv. Math.
\yr 1997
\vol 61
\issue 4
\pages 757--794
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\crossref{https://doi.org/10.1070/im1997v061n04ABEH000137}
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  • https://doi.org/10.1070/im1997v061n04ABEH000137
  • https://www.mathnet.ru/eng/im/v61/i4/p81
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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