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一类具临界指数幂的随机非线性Schrdinger方程

, PP. 285-288

Keywords: 随机非线性Schrdinger方程,白噪声,整体解,基态

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Abstract:

讨论一类带白噪声的随机非线性Schrdinger方程,通过建立方程的性质,运用随机分析方法和Gagliardo-Nirenberg不等式,得到了该方程所对应的初值问题整体解存在的一个充分条件,该条件与一个非线性数量场方程的基态解有关,推广了确定性非线性Schrdinger方程在随机情形下的结论.

References

[1]  Falkovich G E, Kolokolov I, Lebedev V, et al. Statistics of soliton-bearing systems with additive noise[J]. Phys Rev,2001,E63(2):025601.
[2]  Konotop V, Vazquez L. Nonlinear Random Waves[M]. New Jersey:World Scientific Publishing Co Inc,1994.
[3]  Ueda T, Kath W L. Dynamics of optical pulse in randomly birefrengent fibers[J]. Physica,1992,D55:166-181.
[4]  de Bouard A, Debussche A. The stochastic nonlinear Schrdinger equation in H1[J]. Stochastic Analysis and Application,2003,21(1):97-126.
[5]  de Bouard A, Debussche A. Blow-up for the stochastic nonlinear Schrdinger equation with multiplicative noise[J]. The Annals of Probability,2005,33(3):1078-1110.
[6]  Ginibre J, Velo G. On a class of nonlinear Schrdinger equations[J]. J Funct Anal,1979,32:1-71.
[7]  Glassey R T. On the blowup of nonlinear Schrdinger equations[J]. J Math Phys,1977,18(9):1794-1797.
[8]  Ogawa T, Tsutsumi Y. Blow-up of H1 solution for the nonlinear Schrdinger equation[J]. J Diff Eqns,1991,92(2):317-330.
[9]  Ogawa T, Tsutsumi Y. Blow-up of H1 solution for the nonlinear Schrdinger equation with critic power nonlinearity[J]. Proc Am Math Soc,1991,111(2):487-496.
[10]  Weinstein M I. Nonlinear Schrdinger equations and sharp interpolations estimates[J]. Commun Math Phys,1983,87:567-576.
[11]  Sulem C, Sulem P L. The Nonlinear Schrdinger Equation, Self-focusing and Wave Collapse[M]. New York:Springer-Verlag,1999.
[12]  de Bouard A, Debussche A. A stochastic nonlinear Schrdinger equation with multiplcative noise[J]. Commun Math Phys,1999,205:161-181.
[13]  Duan J Q, Lu K N, Bjrn S. Invariant manifolds for stochastic partial differential equations[J]. The Annals of Probability,2003,31(4):2109-2135.
[14]  郭柏灵,王国联,李栋龙. 随机广义Ginzburg-Landau方程的吸引子[J]. 中国科学,2007,A37(12):1429-1437.
[15]  Li Y R, Guo B L. Random attractors for quasi-continuous random dynamical systems and applications to stochastic reaction-diffusion equations[J]. J Diff Eqns,2008,245(7):1775-1800.
[16]  Peter W B, Lu K N, Wang B X. Random attractors for stochastic reaction-diffusion equations on unbounded domains[J]. J Diff Eqns,2009,246(2):845-869.
[17]  Shen Z W, Zhou S F, Shen W X. One-dimensional random attractor and rotation number of the stochastic damped sine-Gordon equation[J]. J Diff Eqns,2010,248(6):1432-1457.
[18]  Bang O, Christiansen P L, Rasmussen K O, et al. Temperature effects in a nonlinear model of monolayer Scheibe aggregates[J]. Phys Rev,1994,E49:4627-4636.
[19]  Bang O, Christiansen P L, Rasmussen K O, et al. White noise in the two-dimensional nonlinear Schrdinger equation[J]. Appl Anal,1995,57:3-15.
[20]  Kwong M K. Uniqueness of positive solutions of Δu-u+up=0 in RN[J]. Arch Ration Mech Anal,1989,105:243-266.
[21]  Cazenave T. An Introduction to Nonlinear Schrdinger Equations[M]. Rio de Janeiro:Textos de Metods Matematicos,1989.
[22]  Zhang J. Stability of attractive Bose-Einstein condensates[J]. J Stat Phys,2000,101(3/4):731-746.

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