Long range scattering for the nonlinear Schrodinger equation with higher order anisotropic dispersion in two dimensions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Saut, Jean-Claude^1,2  Segata, Jun-ichi^3,4 

[1] CNRS, Lab Math, F-91405 Orsay, France

[2] Univ Paris Sud, F-91405 Orsay, France

[3] Tohoku Univ, Math Inst, Aoba Ku, 6-3 Aoba, Sendai, Miyagi 9808578, Japan

[4] Kyushu Univ, Fac Math, Fukuoka, Fukuoka 8190395, Japan

关键词: Schrodinger equation with higher;    order dispersion;    Scattering problem;   

DOI  :  10.1016/j.jmaa.2019.123638

来源: Elsevier

【 摘 要 】

This paper is a continuation of our previous study [13] on the long time behavior of solution to the nonlinear Schrodinger equation with higher order anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS) with the quadratic nonlinearity in two dimensions. More precisely, for a given asymptotic profile u(+), we construct a solution to (4NLS) which converges to u(+) as t -> infinity, where u(+) is given by the leading term of the solution to the linearized equation of (4NLS) with a logarithmic phase correction. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free