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Izvestiya: Mathematics, 2015, Volume 79, Issue 2, Pages 346–374
DOI: https://doi.org/10.1070/IM2015v079n02ABEH002745 (Mi im8179) 		 
This article is cited in 10 scientific papers (total in 10 papers)

The dissipative property of a cubic non-linear Schrödinger equation

P. I. Naumkin

National Autonomous University of Mexico, Institute of Mathematics
English version PDF (400 kB) Citations (10)
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DOI: https://doi.org/10.1070/IM2015v079n02ABEH002745
Abstract: We study the large-time behaviour of solutions of the Cauchy problem for a non-linear Schrödinger equation. We consider the interaction between the resonance term and other types of non-linearity. We prove that solutions exist globally in time and find a large-time asymptotic representation for them. We show that the decay of solutions in the far region has the same order as in the linear case, while the solutions in the short-range region acquire an additional logarithmic decay, which is slower than in the case when there is no resonance term in the original equation.
Keywords: Schrödinger equation, cubic non-linearity, large-time asymptotics.
Received: 22.10.2013
Revised: 04.07.2014
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 2, Pages 137–166
DOI: https://doi.org/10.4213/im8179
Bibliographic databases:
Document Type: Article
UDC: 517.956.8+517.953
MSC: 35Q55, 35C20, 35K15
Language: English
Original paper language: Russian
Citation: P. I. Naumkin, “The dissipative property of a cubic non-linear Schrödinger equation”, Izv. RAN. Ser. Mat., 79:2 (2015), 137–166; Izv. Math., 79:2 (2015), 346–374
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM2015v079n02ABEH002745
  • https://www.mathnet.ru/eng/im/v79/i2/p137
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:470
    Russian version PDF:167
    English version PDF:10
    References:74
    First page:39
     
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