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[1]林成龙,梁宗旗.具波动算子非线性Schrodinger方程行波解的稳定性[J].集美大学学报(自然科学版),2016,21(6):466-470.
　LIN Cheng-long,LIANG Zong-qi.Stability of the Traveling Wave Solutions About the Nonlinear Schrodinger Equation with Wave Operator[J].Journal of Jimei University,2016,21(6):466-470.
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《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

卷:
第21卷
期数:
2016年第6期
页码:
466-470
栏目:
数理科学与信息工程
出版日期:
2016-12-28

文章信息/Info

Title:
Stability of the Traveling Wave Solutions About the Nonlinear Schrodinger Equation with Wave Operator
作者:
林成龙; 梁宗旗
（集美大学理学院，福建 厦门 361021)
Author(s):
LIN Cheng-long; LIANG Zong-qi
(School of Science,Jimei University,Xiamen 361021,China)
关键词:
波动算子; 非线性Schrodinger方程; 拉格朗日方法; 盛金公式; 线性稳定性
Keywords:
wave operator; nonlinear Schrodinger equation; Lagrange method; Shengjin＇s formula; linear stability
分类号:
-
DOI:
-
文献标志码:
A
摘要:
研究具有波动算子的非线性Schrodinger方程的行波解的存在性、不稳定性与色散关系。通过给出该方程Stokes解，在振幅和相位上引入小扰动，来分析行波解的线性稳定性；利用一元四次方程的拉格朗日解法并结合盛金公式对含参数四次方程解的分布情况进行讨论，给出了参数α、β、振幅u0与波数q之间的关系,得到行波解的振荡性、稳定性及不稳定的条件和色散关系。
Abstract:
The existence,stability and dispersion of traveling wave solutions about the nonlinear Schrodinger equation with wave operator were discussed.By giving the Stokes solution of the equation,the small perturbations were introduced into the amplitude and phase to analyze the linear stability of the traveling wave solutions.As the same time,using a quartic equation of Lagrange method and combining with Shengjin＇s formula on distribution with parameter quartic equation solution were discussed,and the relation between the parameters α,β,the amplitude u0 and the wave number q was given,and the oscillation,the stability and the unstable condition and the dispersion relation of the traveling wave solutions were obtained.

参考文献/References:

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相似文献/References:

[1]林成龙,梁宗旗.具波动算子的非线性Schrodinger方程的显式精确解[J].集美大学学报(自然科学版),2017,22(1):67.
　LIN Chenglong,LIANG Zongqi.Explicit and Exact Solutions for NonlinearSchrodinger Equation with Wave Operator[J].Journal of Jimei University,2017,22(6):67.
[2]闫瑞娥,梁宗旗.具波动算子非线性Schrodinger方程线性化差分格式[J].集美大学学报(自然科学版),2020,25(2):146.
　YAN Ruie,LIANG Zongqi.Linearized Difference Scheme for Nonlinear Schrodinger Equation with Wave Operator[J].Journal of Jimei University,2020,25(6):146.

备注/Memo

备注/Memo:
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更新日期/Last Update: 2017-02-21