In this paper, we consider the Fornberg–Whitham equation and a family of solitary wave solutions is found by using minimization principle, where a related penalization function and the concentration-compactness lemma play a key role in the proof. Besides, we also prove that the family of solitary solutions is orbitally stable and decays exponentially when wave speed c is bigger than 1.

中文翻译：

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Fornberg-Whitham方程的孤波的存在和衰减

在本文中，我们考虑了Fornberg-Whitham方程，并使用最小化原理找到了一个孤立波解的族，其中相关的惩罚函数和浓度-紧实性引理在证明中起关键作用。此外，我们还证明了当波速c大于1时，孤立解族在轨道上是稳定的，并且呈指数衰减。