标题： 非线性时依赖一维薛定谔方程，具有双井势 显示英文标题

标题： Nonlinear time-dependent one-dimensional Schroedinger equation with double well potential

摘要： 我们研究了一维具有双井势和外部非线性扰动的时间相关薛定谔方程。 如果初始状态属于由与两个最低特征值相对应的特征向量张成的特征空间，则在半经典极限下，我们证明了将时间相关的方程约化为一个2-模方程可以得到解的主要项，并且可以精确估计误差。 利用这一稳定性结果，我们能够证明对于足够大的非线性强度，会破坏拍动运动。 显示英文摘要

摘要： We consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solution with a precise estimate of the error. By means of this stability result we are able to prove the destruction of the beating motion for large enough nonlinearity.