The paper is concerned with the numerical approximation of the Intermediate Long Wave and Benjamin-Ono systems, that serve as models for the propagation of interfacial internal waves in a two-layer fluid system in particular physical regimes. The paper focuses on two issues of approximation. First, the spectral Fourier-Galerkin method is used to discretize in space the corresponding periodic initial-value problems, and the error of the semidiscretizations is analyzed. The second issue concerns the numerical generation of solitary-wave solutions of the systems. We use acceleration techniques to improve the computation of the approximate solitary waves and check their performance with numerical examples.

翻译：本文关注中长波和本杰明-奥诺系统的数字近似值,它们是在两层流体系统中传播内波的模型,特别是物理系统,侧重于近似的两个问题:第一,利用光谱Fourier-Galerkin方法在空间中分离相应的定期初始值问题,分析了半分解的错误。第二个问题涉及系统单波解决办法的数字生成。我们使用加速技术改进近似单流的计算,并以数字示例检查其性能。