Stability of line standing waves near the bifurcation point for nonlinear Schrödinger equations
Stability of line standing waves near the bifurcation point for nonlinear Schrödinger equations
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非线性薛定谔方程分岔点附近线驻波的稳定性
DOI：
10.2996/kmj/1426684443
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发表时间：
2015
影响因子：
0.6
通讯作者：
Yohei Yamazaki
中科院分区：
文献类型：
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作者：
Yohei Yamazaki
本文考虑R（cid：1）TL上具有幂次非线性项的非线性Schrodinger方程的横向不稳定性，其中2 pL是环面TL的周期.存在一个临界周期2 pLo; p，使得当L <Lo; p时线驻波稳定，当L > Lo; p时线驻波不稳定.本文进一步研究了非线性薛定谔方程线驻波的稳定性与不稳定性从边界L/L o ; p处的分歧.应用Kirr，Kevrekidis和Pelinovsky [16]中的论证和Grillakis，Shatah和Strauss [12]中的方法，我们证明了从线驻波分支出的分支的稳定性。然而，在分歧点处，分歧点附近的线性化算子是退化的。为了证明分歧点的稳定性，我们应用Maeda [18]中的论证。
In this paper we consider the transverse instability for a nonlinear Schro¨dinger equation with power nonlinearity on R (cid:1) T L , where 2 p L is the period of the torus T L . There exists a critical period 2 p L o ; p such that the line standing wave is stable for L < L o ; p and the line standing wave is unstable for L > L o ; p . Here we farther study the bifurcation from the boundary L ¼ L o ; p between the stability and the instability for line standing waves of the nonlinear Schro¨dinger equation. We show the stability for the branch bifurcating from the line standing waves by applying the argument in Kirr, Kevrekidis and Pelinovsky [16] and the method in Grillakis, Shatah and Strauss [12]. However, at the bifurcation point, the linearized operator around the bifurcation point is degenerate. To prove the stability for the bifurcation point, we apply the argument in Maeda [18].
双幂非线性薛定谔方程平稳解的不稳定性
DOI：
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发表时间：
2023
期刊：
影响因子：
--
作者：
Zhen-Qing Chen;Masatoshi Fukushima;Takuya Murayama;Kensuke Yoshizawa;林 興養;Masayuki Hayashi
通讯作者：
Masayuki Hayashi