Publication Cover
Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 3
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Original Articles

Blow-up rate for critical nonlinear Schrödinger equation with Stark potential

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Pages 303-310 | Received 09 Dec 2007, Accepted 16 Jan 2008, Published online: 19 Mar 2008

References

  • Carles , R and Nakamura , Y . 2004 . Nonlinear Schrödinger equations with Stark potential . Hokkaido Math., J. , 33 : 719 – 729 .
  • Cazenave , T . 1993 . “ An introduction to nonlinear Schrödinger equations ” . In Textos de Mètodos Màthmatics , Vol. 26 , Rio de Janeiro : IM-UFRJ .
  • Cycon , HL . 1987 . “ Schrödinger operators with application to quantum mechanics and global geometry ” . In Texts and Monographs in Physics , Berlin : Springer-Verlag .
  • Kwong , MK . 1989 . Uniqueness of positive solutions of ▵u − u + u p = 0 in ℝ N . Arch. Rational. Mech. Anal. , 105 : 243 – 266 .
  • Landam , MJ . 1988 . Rate of blowup for solutions of nonlinear Schrödinger equation at critical dimension . Phys. Rev. A , 38 : 3837 – 3843 .
  • Merle , F and Raphaël , P . 2003 . Sharp upper bound on the blow up rate for critical nonlinear Schrödinger equation . Geom. Funct. Anal. , 13 : 591 – 642 .
  • Merle , F and Raphaël , P . 2004 . On Universality of blow up profile for L 2 critical nonlinear Schrödinger equation . Invent. Math. , 156 : 565 – 672 .
  • Merle , F and Raphaël , P . 2005 . Blow up dynamics and upper bound on the blow up rate for critical nonlinear Schrödinger equation . Annals Math. , 161 : 157 – 222 .
  • Merle , F and Raphaël , P . 2005 . Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation . Comm. Math. Phys. , 253 : 675 – 704 .
  • Merle , F and Raphaël , P . 2005 . On a sharp lower bound on the blow up rate for the L 2 critical nonlinear Schrödinger equation . J. Amer. Soc. , 19 : 37 – 90 .
  • Raphaël , P . 2005 . Stability of log-log bound for blow up solutions to the critical nonlinear Schrödinger equation . Math. Ann. , 331 : 577 – 609 .
  • Tsurumi , T and Wadati , M . 2001 . Free fall of atomic laser beam with weak inter-atomic intercation . J. Phys. Soc. Jpn , 70 : 60 – 68 .

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