The Nonlinear Schrödinger Equation and Applications in Bose-Einstein Condensation and Plasma Physics
The Nonlinear Schrödinger Equation and Applications in Bose-Einstein Condensation and Plasma Physics
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DOI：
10.1142/9789812770226_0003
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
W. Bao;W. Bao
中科院分区：
文献类型：
--
作者：
W. Bao;W. Bao
内容1导论143 2 NLSE由波传播推导144 3 NLSE从BEC 146 3.1无量纲GPE 148 3.2降维148 4 NLSE和变分公式150 4.1守恒律150 4.2拉格朗日结构151 4.3哈密顿结构152 4.4方差恒等式153 5平面和孤立波解NLSE 157 6 NLSE 158 6.1积分存在结果159 6.2存在结果159 6.3有限时间膨胀结果160 7 WKB展开和量子流体动力学161 8 Wigner变换和半经典极限162 9 GPE 164 9.1定态的基态、激发态和中心涡态165
Contents 1 Introduction 143 2 Derivation of NLSE from wave propagation 144 3 Derivation of NLSE from BEC 146 3.1 Dimensionless GPE 148 3.2 Reduction to lower dimension 148 4 The NLSE and variational formulation 150 4.1 Conservation laws 150 4.2 Lagrangian structure 151 4.3 Hamiltonian structure 152 4.4 Variance identity 153 5 Plane and solitary wave solutions of NLSE 157 6 Existence/blowup results of NLSE 158 6.1 Integral form 159 6.2 Existence results 159 6.3 Finite time blowup results 160 7 WKB expansion and quantum hydrodynamics 161 8 Wigner transform and semiclassical limit 162 9 Ground, excited and central vortex states of GPE 164 9.1 Stationary states 165