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关于一类Schrdinger方程的驻波解 被引量:1

On the Standing Waves in a Class of Schrdinger Equations
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摘要 给出了一类描述BoseEinstein 凝聚的非线性Schrdinger This paper gives existence of the standing waves in a class of nonlinear Schrdinger equations which describe the Bose Einstein condensation.
作者 陈渝芝 张健
出处 《四川师范大学学报(自然科学版)》 CAS CSCD 1999年第5期536-540,共5页 Journal of Sichuan Normal University(Natural Science)
关键词 非线性 驻波解 变分法 薛定谔方程 Nonlinear Schrdinger equation Standing wave solution Variational argument
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参考文献3

  • 1Zhang Jian. On the finite-time behaviour for nonlinear Schr?dinger equations[J] 1994,Communications in Mathematical Physics(2):249~260
  • 2Paul H. Rabinowitz. On a class of nonlinear Schr?dinger equations[J] 1992,ZAMP Zeitschrift für angewandte Mathematik und Physik(2):270~291
  • 3Wei-Yue Ding,Wei-Ming Ni. On the existence of positive entire solutions of a semilinear elliptic equation[J] 1986,Archive for Rational Mechanics and Analysis(4):283~308

同被引文献15

  • 1Tsurumi T, Morise H, Wadati M. Stability of Bose - Einstein condensates confined traps [ J ]. International J Modern Physics, 2000,B14(7) :655 -719.
  • 2Zhang J. Stability of attractive Bose - Einstein condensates [ J ]. J Stat Phys, 2000,101 ( 3/4 ) :731 - 746.
  • 3Ding W Y, Ni W M. On the existence of positive entire solutions of a semilinear elliptic equation[ J ]. Arch Rational Meeh Anal, 1986,91:283 - 308.
  • 4Oh Y G. Existence of semiclassical bound states of nonlinear Schr'6dinger equations of the class (V) 2 [ J ]. Commun Part Diff Eqns, 1998,13 (6) : 1499 - 1519.
  • 5Oh Y G. Existence of seminclassieal bound states of nonlinear Schr'6dinger equations with potentials[ J]. Commun Math Phys, 1989,121:11 -33.
  • 6Floer A, Weinstein A. Nonspreading wave packets for the cubic Schr:dinger equation with a bounded potential[ J ]. J Funct Anal, 1986,69:397 -408.
  • 7Zhang J. Stability of standing waves for nonlinear Schr'6dinger equations with unbounded potentials [ J ]. Z Angew Math Phys, 2000,51:498 - 503.
  • 8Grillakis M, Shatah J, Strauss W. Stabihty theory of sohtary waves in the presence of symmetry[J]. J Funct Anal ,1987 ,74 :160 -197.
  • 9Ohberg P, Santos L. Dark solitons in a two- component Bose -Einstein condensate[ J ]. Play Rew Lett ,2001,86(14) :2918 -2921.
  • 10Pu H, Zhang W P, Wilkens M, et al. Phonon spectum and dynamical stability of a dilute quantum degenerate Bose - Fermi mix- ture[J]. Phy Rew Lett,2002,88(7):070408.

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