The Cauchy problem for non-autonomous nonlinear Schroedinger equations

摘要

In this paper we study the Cauchy problem for cubic nonlinear Schrodinger equation with space- and time-dependent coefficients on R~m and T~m. 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.