具有平方反比势的非齐次非线性Schr■dinger方程驻波的强不稳定性

Strong Instability of the Standing Waves for the Inhomogeneous Nonlinear Schr■dinger Equation with Inverse square Potential

讨论一类在三维空间中具有平方反比势的非齐次非线性Schrodinger方程.首先构造一个典型的交叉约束变分问题及几个强制约束变分问题,得到相应的发展不变流形.通过对这些变分问题及发展不变流形的研究,得到爆破解存在的充分条件及其驻波的强不稳定性.

In this paper,we study the focusing cubic inhomogeneous nonlinear Schrdinger equation with inverse-square potential in three dimensions.By constructing a typical cross-constrained variational problem and several constraint variational problems,we get the corresponding invariant evolution flows.Analyzing these variational problems and these invariant evolution flows,the sufficient conditions of the blow-up solutions and the strong instability of the standing waves are obtained for the Cauchy problem.