A detailed numerical study of solutions to the Serre-Green-Naghdi (SGN) equations in 2D with vanishing curl of the velocity field is presented. The transverse stability of line solitary waves, 1D solitary waves being exact solutions of the 2D equations independent of the second variable, is established numerically. The study of localized initial data as well as crossing 1D solitary waves does not give an indication of existence of stable structures in SGN solutions localized in two spatial dimensions. For the numerical experiments, an approach based on a Fourier spectral method with a Krylov subspace technique is applied.

翻译：本文针对速度场旋度为零的二维Serre-Green-Naghdi (SGN)方程解展开详细的数值研究。数值验证了线孤立波（作为第二变量无关的二维方程精确解的一维孤立波）的横向稳定性。对局域初始数据以及一维孤立波交叉的数值实验表明，在二维空间局域化的SGN解中未发现稳定结构存在的迹象。数值实验采用基于傅里叶谱方法与Krylov子空间技术相结合的计算方案。