一类带调和势的非线性Schr(o)dinger方程解的不稳定性

研究了一类带调和势的、与Bose-Einstein凝聚的研究有密切的关系的Schrodinger方程:(iψt=-1/2△ψ+1/2| x |2ψ+f(| ψ|p)ψ)的解.运用能量守衡定律和质量守衡定律和矢量分析的知识,以及积分不等式和解微分不等式的方法,得到了当初值满足一定的条件的柯西问题的解会在有限的时间里发生爆破,推广了已有结论.

On the Instability of Solutions to a Class of Nonliear Schr(o)dinger Equation with Harmonic Potential

A class of Schrodinger equations with harmonic potential:(1 1 iψt= - 1/2△ψ +1/2 | x |2ψ + f( |ψ| p) ψ),which has close relation to Bose-Einstein condensates, is investigated. By using energy conservative law and quality conservative law and knowledge of vector analysis, integral and differential inequality, the author proved that the solution to the Cauchy's problem will blow up in finite time if initial value satisfied with some conditions. The equation in this paper is more general.