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The Asymptotic Behavior of the Stochastic Nonlinear Schrdinger Equation With Multiplicative Noise

The Asymptotic Behavior of the Stochastic Nonlinear Schrdinger Equation With Multiplicative Noise
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摘要 The nonlinear Schrdinger equation is one of the basic models for nonlinear waves.In some circumstances,randomness has to be taken into account and it often occurs through a random potential.Here,we consider the following The nonlinear Schrdinger equation is one of the basic models for nonlinear waves.In some circumstances,randomness has to be taken into account and it often occurs through a random potential.Here,we consider the following equation
作者 王国联
机构地区 The Graduate School of China Academy of Engineering Physics P.O.Box
出处 《数学进展》 CSCD 北大核心 2007年第5期637-639,共3页 Advances in Mathematics（China）
基金 This work was partially supported by Science Foundation of CAEP.
关键词 渐近态 乘性噪音 随机非线性方程 非线性波
分类号 O174.2 [理学—基础数学] O175 [理学—基础数学]
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  • 1Bang, O., Christiansen, P.L., F. If, K.φ. Rasmussen, Temperature effects in a nonlinear model of monolayer Scheibe aggregates, Phys. Rev. EJg, 1994, 4627-4636.
  • 2Ghidaglia, J.M., Finite dimensional behavior for weakly damped driven Schr6dinger equations, Ann. Inst. Henri Poincare, Anal. Non-Lindaire, 1988, 5: 365-405.
  • 3de Bouard, A., Debussche, A., A stochastic nonlinear schrodinger equation with multiplicative noise, Comm. Math. Phys., 1999, 205: 161-181. I
  • 4Yang D., The asymptotic behavior of the stochastic Ginzburg-Landau equation with multiplicative noise, Journal of Mathmatical Physics, 2004, 45(11): 4064-4076.
  • 5Temam, R., Infinite-Dimensional Systems in Mechanics and Physics, Springer-Verlag, New York, 1988.
  • 6Crauel, H. and .Flaudoli, F., Attractors for random dynamical systems, Probab. Theory Relat. Fields, 1994, 100: 365-393.
  • 7Crauel, H., Debussche, A. and Franco, F., Random attractors, Journal of Dynamics and Diferential Equations, 1997, 9(2): 307-341.
  • 8Arnold, L., Random Dynamical System, Springer Monographs in Mathematecs, Springer-Verlag, Berlin, 1998.
  • 9Braszniak, Z., On stochastic convolution in Banach spaces and applications, Stochastics and Stochastic Rep.61, 1997, 245-295.
  • 10Braezniak, Z. and Peszat, S., Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process, Studia Mathematica, 1999, 137: 261-299.
数学进展
2007年 第5期

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