SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 4238-4283, January 2020.
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 $\mathbb{R}^2$, 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.

中文翻译：

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2维Benney-Luke线孤波的稳定性

SIAM数学分析杂志，第52卷，第5期，第4238-4283页，2020年1月。
二维Benney-Luke方程是一个各向同性模型，它描述了3维小振幅的长水波，而KP-II方程是一个横向方向变化缓慢的长波的单向模型。在表面张力弱或微不足道的情况下，水町和岛袋六郎证明了二维Benney-Luke方程的小线孤波的线性稳定性[Nonlinearity，30（2017），第3419--3465页] 。在本文中，我们通过采用Mizumachi的论证[$ \ mathbb {R} ^ 2 $中KP-II方程的线孤子的稳定性，美国数学学会，2015年]，[Proc 。罗伊 Soc。爱丁堡教派。A，148（2018），pp.149--198]，以及在[非线性色散偏微分方程，Springer，纽约，2019，pp。