A numerical approach for the Serre-Green-Naghdi (SGN) equations in 2D based on a Fourier spectral method with a Krylov subspace technique is presented. The code is used to study the transverse stability of line solitary waves, 1D solitary waves being exact solutions of the 2D waves independent of the second variable. The study of localised initial data as well as crossing 1D solitary waves does not give an indication of stable structures in SGN solutions localised in two spatial dimensions.

翻译：本文提出了一种基于傅里叶谱方法与Krylov子空间技术的二维Serre-Green-Naghdi（SGN）方程数值求解方法。该代码用于研究直线孤立波的横向稳定性，其中一维孤立波是二维波动中与第二变量无关的精确解。对局部化初始数据以及一维孤立波交叉现象的研究表明，SGN方程的解中不存在在二维空间上同时局部化的稳定结构。