Asymptotics for the third-order nonlinear Schrödinger equation in the critical case

We consider the Cauchy problem for the third-order nonlinear Schrodinger equation where ℋ=F−1iξξ−1F and F is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition ∫u0xdx≠0. Copyright © 2016 John Wiley & Sons, Ltd.