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

Abstract

We consider the Cauchy problem for the higher-order nonlinear nonlocal Schrödinger equation in one space dimension i∂tu−Λu=λu3u,t>0,x∈R,u0,x=u0x,x∈R,where λ>0, and the linear operator Λu=∑j=351j∂xju. Our purpose in this paper is to prove the large time asymptotic behaviour of solutions for the defocusing case λ>0 with a logarithmic correction under the nonzero mass condition ∫Ru0xdx≠0.