In this paper we study some theoretical and numerical issues of the Boussinesq/Full dispersion system. This is a a three-parameter system of pde's that models the propagation of internal waves along the interface of two-fluid layers with rigid lid condition for the upper layer, and under a Boussinesq regime for the upper layer and a full dispersion regime for the lower layer. We first discretize in space the periodic initial-value problem with a Fourier-Galerkin spectral method and prove error estimates for several ranges of values of the parameters. Solitary waves of the model systems are then studied numerically in several ways. The numerical generation is analyzed by approximating the ode system with periodic boundary conditions for the solitary-wave profiles with a Fourier spectral scheme, implemented in a collocation form, and solving iteratively the corresponding algebraic system in Fourier space with the Petviashvili method accelerated with the minimal polynomial extrapolation technique. Motivated by the numerical results, a new result of existence of solitary waves is proved. In the last part of the paper, the dynamics of these solitary waves is studied computationally, To this end, the semidiscrete systems obtained from the Fourier-Galerkin discretization in space are integrated numerically in time by a Runge-Kutta Composition method of order four. The fully discrete scheme is used to explore numerically the stability of solitary waves, their collisions, and the resolution of other initial conditions into solitary waves.
翻译:在本文中,我们研究的是Boussinesq/Full 的单流分布系统的一些理论和数字问题。 这是一个三参数的粒子系统, 用来模拟在上层两流层界面上, 以及上层布西尼什克制度和下层完全分散制度下, 沿上层两流层的两流层界面, 以及上层布西尼什克制度和下层全面分散制度, 内部波的传播。 我们首先使用Fourier- Galerkin 光谱法在空间中分解定期初始值问题, 并证明对参数数级值的误差估计。 然后用数字方法对模型系统的单流波进行数学研究。 数字系统单流波的新结果以几种方式进行数字化研究。 数字生成的模拟系统, 以四度光谱为间隔的光谱系统, 其尾部的离心结构, 其尾部的离心结构, 其尾部的直径直径的直径结构, 由四度的直径的直径的直径直径分析系统 。