Stability of Benney--Luke Line Solitary Waves in 2 Dimensions
Stability of Benney--Luke Line Solitary Waves in 2 Dimensions
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Benney稳定性--二维卢克线孤立波
DOI：
10.1137/19m1253848
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发表时间：
2020
影响因子：
2
通讯作者：
Shimabukuro Yusuke
中科院分区：
文献类型：
--
作者：
Mizumachi Tetsu;Shimabukuro Yusuke
二维Benney-Luke方程是一个各向同性的模型，它描述了在3维小振幅的长水波，而KP-II方程是一个单向的模型，在横向方向上缓慢变化的长波。在表面张力弱或可忽略的情况下，Mizumachi和Shimabukuro证明了二维Benney-Luke方程的小线孤立波的线性稳定性[Nonlinearity，30（2017），pp. 3419- 3465]。在本文中，我们通过采用Mizumachi [Stability of Line Solitons for the KP-II equation in，American Mathematical Society，2015]，[Proc. Roy. Soc. Edinburgh Sect.A，148（2018），pp. 149- 198]，以及[非线性色散偏微分方程，Springer，纽约，2019年，第149 - 198页。433- 495]证明了KP-II方程单线孤子的非线性稳定性。
The two-dimensional Benney--Luke equation is an isotropic model which describes long water waves of small amplitude in 3 dimensions whereas the KP-II equation is a unidirectional model for long waves with slow variation in the transverse direction. In the case where the surface tension is weak or negligible, linear stability of small line solitary waves of the two-dimensional Benney--Luke equation was proved by Mizumachi and Shimabukuro [Nonlinearity, 30 (2017), pp. 3419--3465]. In this paper, we prove nonlinear stability of the line solitary waves by adopting the argument by Mizumachi [Stability of Line Solitons for the KP-II equation in, American Mathematical Society, 2015], [Proc. Roy. Soc. Edinburgh Sect.A, 148 (2018), pp. 149--198], and in [Nonlinear Dispersive Partial Differential Equations, Springer, New York, 2019, pp. 433--495] which prove nonlinear stability of 1-line solitons for the KP-II equation.