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

Abstract

Abstract We consider the Cauchy problem for the higher-order nonlinear nonlocal Schrodinger equation in one space dimension i ∂ t u − Λ u = λ u 3 u , t > 0 , x ∈ R , u 0 , x = u 0 x , x ∈ R , where λ > 0 , and the linear operator Λ u = ∑ j = 3 5 1 j ∂ x j u . 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 ∫ R u 0 x d x ≠ 0 .