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

We consider the Cauchy problem for the third‐order nonlinear Schrödinger 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...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2017-03, Vol.40 (5), p.1573-1597
Main Authors: Hayashi, Nakao, Kaikina, Elena I.
Format: Article
Language:English
Subjects:
Asymptotic properties
Cauchy problem
Defocusing
Fourier transforms
large time asymptotics
Mathematical analysis
Nonlinearity
Schroedinger equation
Third‐order nonlinear Schrödinger equation
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Summary:We consider the Cauchy problem for the third‐order nonlinear Schrödinger 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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4080