Type: Article

Large time asymptotics for the higher-order nonlinear nonlocal Schrödinger equation

Juárez-Campos, B., Naumkin, P. I.;

Abstract:

We consider the Cauchy problem for the higher-order nonlinear nonlocal Schrödinger equation in one space dimension i?tu??u=?u3u,t>0,x?R,u0,x=u0x,x?R,where ?>0, and the linear operator [Formula presented]. Our purpose in this paper is to prove the large time asymptotic behaviour of solutions for the defocusing case ?>0 with a logarithmic correction under the nonzero mass condition ?Ru0xdx?0.