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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 19
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 2, April 2012
  4. Blow-up profile to solutions of NLS with oscillating nonlinearities
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 6, December 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 5, October 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 4, August 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 3, June 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 2, April 2012
Well-posedness for a mean field model of Ginzburg–Landau vortices with opposite degrees
Mountain pass theorem in ordered Banach spaces and its applications to semilinear elliptic equations
The curve shortening problem under Robin boundary condition
Positive solutions of some parabolic system with cross-diffusion and nonlocal initial conditions
Blow-up profile to solutions of NLS with oscillating nonlinearities
Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 1, February 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Blow-up profile to solutions of NLS with oscillating nonlinearities

Content Provider SpringerLink
Author Zhang, Jian Zhu, Shihui
Copyright Year 2011
Abstract This paper is concerned with the blow-up solutions of nonlinear Schrödinger equation (NLS) with oscillating nonlinearities. The limiting profiles of the blow-up solutions u(t, x) with initial data $${\|u_0\|_{L^2}=\|Q\|_{L^2}}$$ are obtained. It reads that $${|u(t,x)|^2\rightarrow \|Q\|_{L^2}^2\delta_{x=y_1}}$$ (Dirac function), as $${t \rightarrow T}$$ , and that u(t, x) converges strongly to Q(x) in the energy space $${\Sigma=\{u\in H^1; \int |x|^2|u|^2dx<\infty\}}$$ up to scaling and phase parameters and also translation in the nonradial case.
Ending Page 234
Page Count 16
Starting Page 219
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 2
Volume Number 19
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2011-07-08
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Blow-up profile Stability Analysis Oscillating nonlinearity Blow-up solution Nonlinear Schrödinger equation NLS-like equations (nonlinear Schrödinger)
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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