In this paper, the two-component Fornberg–Whitham system is studied. We first investigate the local well-posedness in classical Sobolev space and establish a blow-up criterion by a local-in-time priori estimate, and then, we give some sufficient conditions on the initial data to lead to wave breaking. Finally, we discuss analytically the existence of periodic traveling waves by the bifurcation theorem.

中文翻译：

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两成分的Fornberg-Whitham系统的适定性，爆炸波和行波

在本文中，研究了由两部分组成的Fornberg-Whitham系统。我们首先研究经典Sobolev空间中的局部适定性，并通过局部时间先验估计建立爆炸标准，然后为初始数据提供一定条件以导致波浪破裂。最后，我们通过分叉定理分析地讨论了周期性行波的存在。