The Cauchy problem for non-autonomous nonlinear Schr(o)dinger equations  

作　　者：Peter Y. H. Pang 

机构地区：[1]Department of Mathematics

出　　处：《Science China Mathematics》2005年第4期522-538,共17页中国科学：数学（英文版）

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.

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.

关 键 词：NON-AUTONOMOUS Schr(o)dinger equations  LOCAL existence  GLOBAL existence. 

分 类 号：O175[理学—数学]