期刊文献+

一类带无界势的非线性Schrdinger方程的整体解 被引量:3

The Global Solutions for Nonlinear Schrdinger Equations with Unbounded Potentials
下载PDF
导出
摘要 对于描述玻色-爱因斯坦凝聚的带无界势的非线性Schrdinger方程,证明了解整体存在的充分条件,并且该条件与方程的基态解密切相关. For the nonlinear Schroedinger equations with unbounded potentials which describe Bose-Einstein condensates, a sufficient condition for the existence of global solutions is given, and this condition is closely related to the ground state solution.
作者 刘倩 张健
出处 《四川师范大学学报(自然科学版)》 CAS CSCD 北大核心 2005年第4期394-396,共3页 Journal of Sichuan Normal University(Natural Science)
基金 国家自然科学基金(10271084) 四川省杰出青年学科带头人基金资助项目
关键词 无界势 非线性SCHROEDINGER方程 整体解 玻色-爱因斯坦凝聚 基态解 Unbounded potential Nonlinear Schroedinger equation Global solution Bose-Einstein condensate Ground state solution
  • 相关文献

参考文献16

  • 1Weinstein M I.Nonlinear Schrodinger equations and sharp interpolation estimate[J].Commun Math Phys,1983,87:567~576.
  • 2Zhang J.Sharp conditions of global existence for nonlinear Schr(o)dinger and Klein-Gordon equations[J].Nonlinear Analysis TMA,2002,48:191~207.
  • 3Merle F.Nonexistence of minimal blow-up solutions of equations iut=-Δu-k(x)|u|4/n in R^n[J].Ann Inst Henri Poincaré Phsique Théorique,1996,64(1):33~85.
  • 4Ding W Y, Ni W M.On the existence of positive entire solutions of a semilinear elliptic equation[J].Arch Rational Mech Anal,1986,91:283~308.
  • 5Wang X F, Zeng B.On concentration of positive bound states of nonlinear Schr(o)dinger equations with competing potential functions[J].SIAM J Math Anal,1997,28:633~655.
  • 6舒级,张健.一类带阻尼项的Gross-Pitaevskii方程在二维空间中的坍塌性质[J].四川师范大学学报(自然科学版),2003,26(2):120-123. 被引量:22
  • 7Bradley C C, Sackett C A, Hulet R G.Bose-Einstein condensation of lithium: Observation of limited condensate number[J].Phys Rev Lett,1997,78: 985~989.
  • 8Wadati M, Tsurumi T.Critical number of atoms for the magnetically trapped Bose-Einstein condensate with negative s-wave scattering length[J].Phys Lett,1998,A247:287~293.
  • 9Zhang J.Stability of attractive Bose-Einstein condensates[J].J Statistical Physics,2000,101:731~746.
  • 10Zhang J.Stability of standing waves for nonlinear Schrodinger equations with unbounded potentials[J].Z Angew Math Phys,2000,51:498~503.

二级参考文献71

  • 1[23]Glassey R T. On the blowing up of solutions to the Cauchy problem for nonlinear Schrodinger equations[J]. J Math Phys, 1977,18(9):1794~1797.
  • 2[24]Oh Yong-Geum. Cauchy problem and Ehrenfest' s law of nonlinear Schrodinger equation with potentials[J]. J Diff Equ, 1989,81:255~274.
  • 3[25]Cazenave T. An introduction to nonlinear Schrodinger equations[M]. Riede Janerro:Textos de Metodos Matematicos, 1989.48 ~ 73.
  • 4[1]Bradley C C, Sackett C A, Hulet R G. Bose-Einstein condensation of lithium:observation of limited condensate number[J]. Phys Rev Lett, 1997,78:985 ~ 989.
  • 5[2]Dalfove F, Giorgini S, Pitaevskii Lev P. Theory of Bose-Einstein condensation in trapped gases[J]. Rev Modern Phys, 1999,71 (3): 463~512.
  • 6[3]Huepe C, Métems S, Dewel G, et al. Decay rates in attractive Bose-Einstein condensates[J]. Phys Rev Lett, 1999,82:1616 ~ 1619.
  • 7[4]Kagan Y, Muryshev A E, Shlyapnikov G V. Collapse and Bose-Einstein condensation in a trapped Bose gas with negative scattering length [J]. Phys Rev Lett,1998,81(5) :933 ~937.
  • 8[5]Wadati M, Tsurumit T. Critical number of atoms for the magnetically trapped Bose-Einstein condensation with negative s-wave scattering length[J]. Phys Lett, 1998,247A:287~293.
  • 9[6]Tsurumit T, Wadati M. Collapse of wave functions in multidimensions nonlinear Schrodinger equations under harmonic potential[J]. Phys Soc Jpn, 1997,66:3031~3034.
  • 10[7]Saito H, Ueda M. Inter-mittent implosion and pattern formation of trapped Bose-Einstein condensates with an attractive interaction[J].Phys Rev Lett,2001,86(8): 1406~ 1409.

共引文献29

同被引文献20

引证文献3

二级引证文献4

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部