The existence of a new type of cusped solitary wave, which decays algebraically at infinity, for a nonlinear equation modeling the free surface evolution of moderate amplitude waves in shallow water is established by employing qualitative analysis for differential equations. Furthermore, the exact parametric representation as well as its planar graph for such type of wave is also given.

中文翻译：

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由中等振幅表面波方程控制的具有代数衰减的尖峰孤立波

通过对微分方程进行定性分析，建立了模拟浅水中中等振幅波自由表面演化的非线性方程，存在一种在无穷远代数衰减的新型尖角孤立波。此外，还给出了此类波的精确参数表示及其平面图。