n维空间中一类耦合系统解的爆破性质

The Blow-up of Solutions to a Class of the Coupled System in n-dimension

采用Tsutsumi和Zhang ( Adv. Math. Sci. Appl., 1998, 10: 232-246 ) 和Weinstein等(Comm. Math. phys., 1983, 87: 567-576.)的方法,研究了一类非线性 Schr dinger 方程耦合系统()yqyyyy=+D+2Fit,,22yqq=+D-a(()()txtx,,qy和分别为复值和实值函数,0,,>tRxRan)的初值问题,得到在n维空间中当()()xx00,yy=时解的爆破性质。

By using methods initiated by Tsutsumi, Zhang (Adv. Math. Sci. Appl. 1998, 10: 232~246.) and Weinstein etc. (Comm. Math. Phys., 1983, 87: 567-576. ), the following intial-value problem for the coupled system of the nonlinear Schr鰀inger equations is studied: ()yqyyyy=+D+2Fit , ,22yqq=+D-a where ()tx,y and ()tx,q are complex and real-value functions respectively and 0,,ftRxRan .The blow-up of the solution of the system in n-dimension is obtained.