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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2013, Issue 1(30), Pages 159–171
DOI: https://doi.org/10.14498/vsgtu1159 (Mi vsgtu1159) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

Blow-up of solutions of Cauchy problem for nonlinear Schrödinger equation

V. Zh. Sakbaev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, 141700, Russia
Full-text PDF (214 kB) Citations (2)
(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu1159
Abstract: In this work we study the effect of time finiteness of the existence of Cauchy problem for nonlinear Schrödinger equation solution. Together with the ill-posed Cauchy problem we consider its neighborhood in the space of operators, representing Cauchy problem. We explore the convergence of sequence of solutions of Cauchy problems with the operators, approximating the initial Hamiltonian.
Keywords: nonlinear Schrödinger equation, regularization, blow-up regime, blow-up of solution, viscosity solution.
Original article submitted 12/XI/2012
revision submitted – 01/II/2013
Bibliographic databases:
Document Type: Article
UDC: 517.958:530.145.6
MSC: Primary 46N50; Secondary 81S15, 81P15
Language: Russian
Citation: V. Zh. Sakbaev, “Blow-up of solutions of Cauchy problem for nonlinear Schrödinger equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 159–171
Citation in format AMSBIB
\Bibitem{Sak13}
\by V.~Zh.~Sakbaev
\paper Blow-up of solutions of Cauchy problem for nonlinear Schr\"odinger equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 1(30)
\pages 159--171
\mathnet{http://mi.mathnet.ru/vsgtu1159}
\crossref{https://doi.org/10.14498/vsgtu1159}
Linking options:
  • https://www.mathnet.ru/eng/vsgtu1159
  • https://www.mathnet.ru/eng/vsgtu/v130/p159
    • This publication is cited in the following 2 articles:
    1. Efremova L.S., Grekhneva A.D., Sakbaev V.Zh., “Phase Flows Generated By Cauchy Problem For Nonlinear Schrodinger Equation and Dynamical Mappings of Quantum States”, Lobachevskii J. Math., 40:10, SI (2019), 1455–1469  crossref  mathscinet  zmath  isi  scopus
    2. V. Zh. Sakbaev, “Gradient blow-up of solutions to the Cauchy problem for the Schrödinger equation”, Proc. Steklov Inst. Math., 283 (2013), 165–180  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Abstract page:840
    Full-text PDF :376
    References:104
    First page:1
     
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