Type: Article

Global existence of solutions for a subcritical nonlinear Schrödinger equation

Hayashi, Nakao; Naumkin, Pavel I.;

Abstract:

Abstract We consider the one dimensional nonlinear Schrödinger equation View the MathML source{iut+12uxx=N(u,u¯),x?R,t>1,u(1,x)=u0(x),x?R, where the nonlinearity View the MathML sourceN(u,u¯)=|u|?2?u3=u3?2?u¯?2?, the exponent ?>0?>0 is sufficiently small. Our purpose in this paper is to prove a global existence in time of small solutions.