[1] | Sulem C, Sulem P L. The Nonlinear Schr?dinger Equation[M]. New York:Springer-Verlag,1999.
|
[2] | Chen T, Pavlovic N. The quintic NLS as the mean field limit of a Boson gas with three-body interactions[J]. J Functional Anal,2011,260(4):959-997.
|
[3] | Cazenave T. Semilinear Schr?dinger Equations:Courant Lecture Notes in Mathematics[M]. New York:New York University, Courant Institute Math Sciences,2003.
|
[4] | Tao T. Nonlinear dispersive equations:local and global analysis[C]//CBMS Regional Conference Series in Math. New York:AMS,2006.
|
[5] | Fujiwara D. A construction of the fundamental solution for the Schr?dinger equation[J]. J Analyse Math,1979,35(1):4-96.
|
[6] | Oh Y G. Cauchy problem and ehrenfest's law of nonlinear Schr?dinger equations with potentials[J]. J Diff Eqns,1989,81(2):255-274.
|
[7] | Zhang J. Stability of attractive Bose-Einstein condensates[J]. J Statist Phys,2000,101(3/4):731-746.
|
[8] | Carles R. Remarks on nonlinear Schr?dinger equations with harmonic potential[J]. Ann Henri Poincare:AN,2002,3(4):757-772.
|
[9] | Carles R. Nonlinear Schr?dinger equations with repulsive harmonic potential and applications[J]. SIAM J Math Anal,2003,35(4):823-843.
|
[10] | Carles R. Linear vs. nonlinear effects for nonlinear Schr?dinger equations with potential[J]. Commun Contemp Math,2005,7(4):483-508.
|
[11] | Carles R. Global existence results for nonlinear Schr?dinger equations with quadratic potentials[J]. Discrete Contin Dyn Syst,2005,13(2):385-398.
|
[12] | 喻朝阳. 四阶非线性波方程整体解的存在唯一性[J]. 重庆师范大学学报:自然科学版,2014,31(5):95-99.
|
[13] | 周鑫,胡先权. 球谐环形振荡势薛定谔方程的精确解[J]. 重庆师范大学学报:自然科学版,2011,28(5):63-67.
|
[14] | Wadati M, Tsurumi T. Collapse of wavefunctions in multi-dimensional nonlinear Schr?dinger equations under harmonic potential[J]. J Phys Soc Jpn,1997,66(10):3031-3034.
|
[15] | Saito H, Ueda M. Intermittent implosion and pattern formation of trapped Bose-Einstein condensates with an attractive interaction[J]. Phys Rev Lett,2001,86(8):1406-1409.
|
[16] | Adhikari S K. Evolution of a collapse and exploding Bose-Einstein condensate in different trap symmetries[J]. Phys Rev,2005,A71(5):1-8.
|
[17] | Adhikari S K. Dynamics of a collapsing and exploding Bose-Einstein condensed vortex state[J]. Phys Rev,2002,A66(4):1-7.
|
[18] | Bergé L, Rasmussen J J. Collapsing dynamics of attractive Bose-Einstein condensates[J]. Phys Lett,2002,A304(5/6):136-142.
|
[19] | Dalfovo F, Giorgini S, Pitaevskii P L, et al. Theory of Bose-Einstein condensation in trapped gases[J]. Rev Modern Phys,1999,71(3):463-512.
|
[20] | Gérard P. The Cauchy problem for the Gross-Pitaevskii equation[J]. Ann I H Poincaré:AN,2006,23(5):765-779.
|
[21] | Pelinovsky D, Schneider G. Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential[J]. J Diff Eq,2010,248(4):837-849.
|
[22] | Ohta M, Todorova G. Remarks on global existence and blowup for damped nonlinear Schr?dinger equations[J]. Discrete Contin Dyn Syst,2009,23(4):1313-1325.
|
[23] | Tsutsumi M. Nonexistence of global solutions to the Cauchy problem for the damped nonlinear Schr?dinger equations[J]. SIAM J Math Anal,1984,15(2):357-366.
|
[24] | Fibich G. Self focusing in the damped nonlinear Schr?dinger equation[J]. SIAM J Appl Math,2001,61(5):1680-1705.
|
[25] | Goubet O. Asymptotic smoothing effect for a weakly damped nonlinear Schr?dinger equation in T
|
[26] | [J]. J Diff Eqns,2000,165(1):96-122.
|
[27] | Laurencot P. Long-time behaviour for weakly damped driven nonlinear Schr?dinger equations in R
|
[28] | . NoDEA Nonlin Diff Eqns Appl,1995,2(3):357-369.
|
[29] | Kita N, Shimomura A. Asymptotic behavior of solutions to Schr?dinger equations with a subcritical dissipative nonlinearity[J]. J Diff Eqns,2007,242(1):192-210.
|
[30] | Shimomura A. Asymptotic behavior of solutions for Schr?dinger equations with dissipative nonlinearities[J]. Commun Part Diff Eqns,2006,31(9):1407-1423.
|
[31] | 罗光. 浅析自由粒子的薛定谔方程的解[J]. 重庆师范大学学报:自然科学版,2014,31(2):77-79.
|
[32] | Passot T, Sulem C, Sulem P L. Linear versus nonlinear dissipation for critical NLS equation[J]. Physica,2005,D203(3/4):167-184.
|
[33] | Antonelli P, Christof S. Global well-posedness for cubic NLS with monlinear damping[J]. Commun Part Diff Eqns,2010,35(12):2310-2328.
|
[34] | Biswas E A. Optical soliton perturbation with nonlinear damping and saturable amplifiers[J]. Math Comput Simul,2001,56(6):521-537.
|
[35] | Pereira N R, Steno L. Nonlinear Schr?dinger equation including growth and damping[J]. Phys Fluids,1977,20(10):1733-1734.
|
[36] | 罗光. 浅析自由粒子的薛定谔方程的解[J]. 重庆师范大学学报:自然科学版,2014,31(2):77-79.
|
[37] | Antonelli P, Marcati P. On the finite energy weak solutions to a system in quantum fluid dynamics[J]. Commun Math Phys,2009,287(2):657-686.
|
[38] | 丁凌, 周良金, 张丹丹. 在混合边界条件下临界指数的椭圆方程的解[J]. 四川师范大学学报:自然科学版,2011,34(4):521-527.
|
[39] | Gasser I, Markowich P A. Quantum hydrodynamics, wigner transforms and the classical limit[J]. Asympt Anal,1997,14(2):97-116.
|
[40] | Carles R. Semi-classical Schr?dinger equations with harmonic potential and nonlinear perturbation[J]. Annales Inst Henry Poincore:AN,2003,20(3):501-542.
|
[41] | Colliander J, Keel M, Staffilani G, et al. Global well-posedness and scattering for the energy-critical nonlinear Schrodinger equation in R
|
[42] | [J]. Ann Math,2008,167(3):767-865.
|
[43] | Killip R, Visan M, Zhang X Y. Energy-critical NLS with quadratic potentials[J]. Commun Part Diff Eqns,2009,34(10/11/12):1531-1565.
|