2019/04/01 by Tetsu Mizumachi, Mizumachi, Tetsu, Yusuke Shimabukuro +1 · 2 citations
Mathematics · Physics and Astronomy · #37K45 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Primary 35B35 #Secondary 35Q35
paper · pdf · doi:10.48550/arxiv.1904.01142
openalex publication_date 2019/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 2D Benney-Luke equation is an isotropic model which describes long water waves of small amplitude in 3D 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, linearly stability of small line solitary waves of the 2D Benney-Luke equation was proved by Mizumachi and Shimabukuro [Nonlinearity, 30 (2017), 3419--3465]. In this paper, we prove nonlinear stability of the line solitary waves by adopting the argument by Mizumachi ([Mem. Amer. Math. Soc. no. 1125], [Proc. Roy. Soc. Edinburgh Sect. A., 148 (2018), 149--198] and [arXiv:1808.00809]) which prove nonlinear stability of 1-line solitons for the KP-II equation.