Journal of Nonlinear Mathematical Physics

Volume 27, Issue 4, September 2020, Pages 592 - 615

Asymptotics behavior for the integrable nonlinear Schrödinger equation with quartic terms: Cauchy problem

Authors
Lin Huang
School of Science, Hangzhou Dianzi University, Hangzhou 310018, P. R. China, lin.huang@hdu.edu.cn & linhuang@kth.se
Received 10 August 2019, Accepted 3 January 2020, Available Online 4 September 2020.
DOI
https://doi.org/10.1080/14029251.2020.1819605How to use a DOI?
Keywords
Integrable nonlinear Schrödinger equation with quartic terms, Long-time asymptotics, Nonlinear steepest descent method
Abstract

We consider the Cauchy problem of integrable nonlinear Schrödinger equation with quartic terms on the line. The first part of the paper considers the Riemann-Hilbert formula via the unified method(also known as the Fokas method). The second part of the paper establishes asymptotic formulas for the solution of initial value problem using the nonlinear steepest descent method(also known as the Deift-Zhou method).

Copyright
© 2020 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 4
Pages
592 - 615
Publication Date
2020/09
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2020.1819605How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Lin Huang
PY  - 2020
DA  - 2020/09
TI  - Asymptotics behavior for the integrable nonlinear Schrödinger equation with quartic terms: Cauchy problem
JO  - Journal of Nonlinear Mathematical Physics
SP  - 592
EP  - 615
VL  - 27
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1819605
DO  - https://doi.org/10.1080/14029251.2020.1819605
ID  - Huang2020
ER  -