摘要
In this paper we study the Cauchy problem for cubic nonlinear Schr(o)dinger equation with space-and time-dependent coefficients on Rm and Tm. By an approximation argument we prove that for suitable initial values, the Cauchy problem admits unique local solutions. Global existence is discussed in the cases of m=1,2.
In this paper we study the Cauchy problem for cubic nonlinear Schrodinger equation with space- and time-dependent coefficients on Rm and Tm. By an approximation argument we prove that for suitable initial values, the Cauchy problem admits unique local solutions. Global existence is discussed in the cases of m = 1,2.
基金
This work was supported in part by National University of Singapore Academic Research Fund Grant R-146-000-034-112
Wang Youde was further supported in part by the National Key Basic Research Fund G1999075107
the National Science Fund for Distinguished Young Scholars 10025104 of the People's Republic of China.
