Davey A, Stewartson K. On three-dimensional packets of surfaces waves[J]. Proc Royal Soc,1974,A338:101-110.
[2]
Wadati 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.
[3]
Zhang J. Stability of attractive Bose-Einstein condensate[J]. J Stat Phys,2000,10(1):731-746.
[4]
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]
Cazenave T. Semilinear Schr？dinger equations[C]//Courant Lecture Notes in Mathematics,10. NYU:CIMS,AMS,2003.
[6]
Oh Y G. Cauchy problem and Ehrenfest’s law of nonlinear Schr？dinger equations with potentials[J]. J Diff Eqns,1989,81:255-274.
[7]
Zhang J. Sharp threshold for blowup and global existence in nonlinear Schr？dinger equations under a harmonic potential[J]. Commun PDE,2005,30:1429-1443.
[8]
Shu J, Zhang J. Nonlinear Schr？dinger equation with harmonic potential[J]. J Math Phys,2006,47:063503-1-6.
[9]
Chen G G, Zhang J. Sharp threshold of global existence for nonlinear Gross-Pitaevskii equation in RN[J]. IMA J Appl Math,2006,71:232-240.
[10]
Carles R. Critical nonlinear Schr？dinger equations with and without harmonic potential[J]. Math Models Methods Appl Sci,2002,12:1513-1523.
[11]
Merle F, Rapha？l P. On universality of blow-up profile for L2 critical nonlinear Schr？dinger equation[J]. Invent Math,2004,156:565-672.
[12]
Merle F, Rapha？l P. Blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr？dinger equation[J]. Ann Math,2005,16:157-222.
[13]
Merle F, Rapha？l P. On a sharp lower bound on the blow-up rate for the L2-critical nonlinear Schr？dinger equation[J]. J Amer Math Soc,2006,19:37-90.
[14]
Li X G, Zhang J. Limit behavior of blow-up solutions for critical nonlinear Schr？dinger equation with harmonic potential[J]. Diff Integral Eqns,2006,19:761-771.
[15]
Li X G, Zhang J, Wu Y H. Mathematical analysis of the collapse in Bose-Einstein Condensate[J]. Acta Math Sci,2009,B29:56-64.
[16]
Zhang J, Li X G, Wu Y H. Remarks on the blow-up rate for critical nonlinear Schr？dinger equation with harmonic potential[J]. Appl Math Comput,2009,208:389-396.
[17]
Zhu S H, Zhang J, Li X G. Limiting profile of blow-up solutions for the Gross-Pitaevskii equation[J]. Sci China:Math,2009,A52:1017-1030.
[18]
Ghidaglia J M, Saut J C. On the initial value problem for the Davey-Stewartson systems[J]. Nonlinearity,1990,3:475-506.
[19]
Guo B L, Wang B X. The Cauchy problem for Davey-Stewartson systems[J]. Commun Pure Appl Math,1999,52:1477-1490.
[20]
Sulem C, Sulem P L. The nonlinear Schr？dinger equation:Self-focusing and wave collapse[C]//Appl Math Sci,139. New York:Springer-Verlag,1999.
[21]
Cipolatti R. On the existence of standing waves for a Davey-Stewartson system[J]. Commun PDE,1992,17:967-988.
[22]
Zhang J, Zhu S H. Sharp blow-up criteria for the Davey-Stewartson system in R3[J]. Dynamics PDE,2011,8:239-260.
[23]
Cipolatti R. On the instability of ground states for a Davey-Stewartson system[J]. Ann Inst Henri Poincaré: Phys Theor,1993,58:85-104.
[24]
Ohta M. Stability of standing waves for the generalized Davey-Stewartson system[J]. J Dynam Diff Eqns,1994,6:325-334.
[25]
Ohta M. Instability of standing waves the generalized Davey-Stewartson systems[J]. Ann Inst Henri Poincare: Phys Theor,1995,63:69-80.
[26]
Gan Z H, Zhang J. Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system[J]. Commun Math Phys,2008,283:93-125.
[27]
Wang B X, Guo B L. On the initial value problem and scattering of solutions for the generalized Davey-Stewartson systems[J]. Sci China:Math,2001,A44:994-1002.
[28]
Ozawa T. Exact blow-up solutions to the Cauchy problem for the Davey-Stewartson systems[J]. Proc Roy Soc London,1992,A436:345-349.
[29]
Richards G. Mass concentration for the Davey-Stewartson system[J]. Diff Integral Eqns,2011,24:261-280.
[30]
Papanicolaou G C, Sulem C, Sulem P L, et al. The focusing singularity of the Davey-Stewartson equations for gravity-capillary surface waves[J]. Physica,1994,D72:61-86.
[31]
Gan Z H, Zhang J. Sharp conditions of global existence for the generalized Davey-Stewartson system in three dimensional space[J]. Acta Math Scientia,2006,A26:87-92.
[32]
Shu J, Zhang J. Sharp conditions of global existence for the generalized Davey-Stewartson system[J]. IMA J Appl Math,2007,72:36-42.
[33]
Li X G, Zhang J, Lai S Y, et al. The sharp threshold and limiting profile of blow-up solutions for a Davey-Stewartson system[J]. J Diff Eqns,2011,250:2197-2226.
[34]
Gérard P. Description du defaut de compacite de l’injection de Sobolev[J]. ESAIM Control Optim Calc Var,1998,3:213-233.
[35]
Hmidi T, Keraani S. Blowup theory for the critical nonlinear Schr？dinger equations revisited[J]. Internat Math Res Notices,2005,46:2815-2828.
[36]
Weinstein M I. Nonlinear Schr？dinger equations and sharp interpolation estimates[J]. Commun Math Phys,1983,87:567-576.
[37]
Zhang J. Cross-constrained variational problem and nonlinear Schr？dinger equation[C]//Cucker F, Rojas J M. Proc Smalefest 2000. Found Comput Math. New Jersey:World Scientific,2002.
[38]
Zhang J. Sharp conditions of global existence for nonlinear Schr？dinger and Klein-Gordon equations[J]. Nonlinear Anal,2002,48:191-207.
[39]
Holmer J, Roudenko S. On blow-up solutions to the 3D cubic nonlinear Schr？dinger equation[J]. Appl Math Research Express,2007,2007:4.
[40]
Kwong M K. Uniqueness of positive solutions of Δu-u +up=0 in Rn[J]. Arch Rational Mech Anal,1989,105:243-266.
[41]
Strauss W A. Existence of solitary waves in higher dimensions[J]. Commun Math Phys,1977,55:149-162.
