时间周期边界条件下聚焦 Kundu-Eckhaus 方程的渐近孤子

Xiu Bin Wang; Yong Chen; Shou Fu Tian; Zhen Wu Fu; Jin Jie Yang; Zhi Qiang Li

doi:10.1360/SSM-2022-0162

时间周期边界条件下聚焦 Kundu-Eckhaus 方程的渐近孤子

Translated title of the contribution: Asymptotic solitons of the focusing Kundu-Eckhaus equation with time-periodic boundary condition

Xiu Bin Wang
, Yong Chen^*
, Shou Fu Tian^*
, Zhen Wu Fu
, Jin Jie Yang
, Zhi Qiang Li

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we investigate the focusing Kundu-Eckhaus equation on the quarter plane. The initial data vanish at infinity while the boundary data are time-periodic, which are of the form ae^iδe^2iωt. Firstly, we derive a Riemann-Hilbert problem whose solution yields the solution to our IBV (initial boundary value) problem. Moreover, we find that for ω < −3a²/2−3β²a⁴, the solution of the IBV problem has different asymptotic behaviors in different regions. In particular, for the asymptotic solitons region, the solution of the IBV problem is asymptotic to a series of asymptotic solitons.

Translated title of the contribution	Asymptotic solitons of the focusing Kundu-Eckhaus equation with time-periodic boundary condition
Original language	Chinese (Traditional)
Pages (from-to)	737-750
Number of pages	14
Journal	Scientia Sinica Mathematica
Volume	53
Issue number	5
DOIs	https://doi.org/10.1360/SSM-2022-0162
State	Published - 2023

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title = "时间周期边界条件下聚焦 Kundu-Eckhaus 方程的渐近孤子",

abstract = "In this paper, we investigate the focusing Kundu-Eckhaus equation on the quarter plane. The initial data vanish at infinity while the boundary data are time-periodic, which are of the form aeiδe2iωt. Firstly, we derive a Riemann-Hilbert problem whose solution yields the solution to our IBV (initial boundary value) problem. Moreover, we find that for ω < −3a2/2−3β2a4, the solution of the IBV problem has different asymptotic behaviors in different regions. In particular, for the asymptotic solitons region, the solution of the IBV problem is asymptotic to a series of asymptotic solitons.",

keywords = "Riemann-Hilbert problem, asymptotic soliton, the focusing Kundu-Eckhaus equation, time-periodic boundary condition",

author = "Wang, \{Xiu Bin\} and Yong Chen and Tian, \{Shou Fu\} and Fu, \{Zhen Wu\} and Yang, \{Jin Jie\} and Li, \{Zhi Qiang\}",

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T1 - 时间周期边界条件下聚焦 Kundu-Eckhaus 方程的渐近孤子

AU - Wang, Xiu Bin

AU - Chen, Yong

AU - Tian, Shou Fu

AU - Fu, Zhen Wu

AU - Yang, Jin Jie

AU - Li, Zhi Qiang

PY - 2023

Y1 - 2023

N2 - In this paper, we investigate the focusing Kundu-Eckhaus equation on the quarter plane. The initial data vanish at infinity while the boundary data are time-periodic, which are of the form aeiδe2iωt. Firstly, we derive a Riemann-Hilbert problem whose solution yields the solution to our IBV (initial boundary value) problem. Moreover, we find that for ω < −3a2/2−3β2a4, the solution of the IBV problem has different asymptotic behaviors in different regions. In particular, for the asymptotic solitons region, the solution of the IBV problem is asymptotic to a series of asymptotic solitons.

AB - In this paper, we investigate the focusing Kundu-Eckhaus equation on the quarter plane. The initial data vanish at infinity while the boundary data are time-periodic, which are of the form aeiδe2iωt. Firstly, we derive a Riemann-Hilbert problem whose solution yields the solution to our IBV (initial boundary value) problem. Moreover, we find that for ω < −3a2/2−3β2a4, the solution of the IBV problem has different asymptotic behaviors in different regions. In particular, for the asymptotic solitons region, the solution of the IBV problem is asymptotic to a series of asymptotic solitons.

KW - Riemann-Hilbert problem

KW - asymptotic soliton

KW - the focusing Kundu-Eckhaus equation

KW - time-periodic boundary condition

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DO - 10.1360/SSM-2022-0162

M3 - 文章

AN - SCOPUS:85160398574

SN - 1674-7216

VL - 53

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JO - Scientia Sinica Mathematica

JF - Scientia Sinica Mathematica

IS - 5

ER -

时间周期边界条件下聚焦 Kundu-Eckhaus 方程的渐近孤子

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