Asymptotic linear stability of Benney–Luke line solitary waves in 2D
Asymptotic linear stability of Benney–Luke line solitary waves in 2D
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二维 Benney-Luke 线孤立波的渐近线性稳定性
DOI：
10.1088/1361-6544/aa7cc7
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发表时间：
2017
期刊：
影响因子：
1.7
通讯作者：
Yusuke Shimabukuro
中科院分区：
文献类型：
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作者：
Tetsu Mizumachi;Yusuke Shimabukuro
本文研究了二维Benney-Luke方程的线孤立波的横向线性稳定性。在表面张力弱或可忽略的情况下，我们发现线性化算子在λ=0附近的共振连续本征值曲线。这些共振连续本征模的时间演化描述的一维阻尼波方程的横向变量，它给出了一个线性近似的调制线孤立波的局部相移。在权函数沿线孤立波运动方向增加的指数加权空间中，线性化方程的另一部分解随t→∞指数衰减.
In this paper, we study transverse linear stability of line solitary waves to the two-dimensional Benney–Luke equation which arises in the study of small amplitude long water waves in 3D. In the case where the surface tension is weak or negligible, we find a curve of resonant continuous eigenvalues of the linearized operator in a neighborhood of λ=0. Time evolution of these resonant continuous eigenmodes is described by a 1D damped wave equation in the transverse variable and it gives a linear approximation of the local phase shifts of modulating line solitary waves. In exponentially weighted space whose weight function increases in the direction of the motion of the line solitary wave, the other part of solutions to the linearized equation decays exponentially as t→∞.
能量空间中晶格孤子的渐近稳定性
DOI：
--
发表时间：
2008
期刊：
影响因子：
--
作者：
T.;Mizumachi
通讯作者：
Mizumachi