On periodic solutions of interfacial waves of finite amplitude

Using the two-layer fluid model for long interfacial waves of finite amplitude, we find solutions for periodic traveling waves and investigate their properties. In addition, it is shown that these periodic traveling waves can be represented as an infinite sum of spatially repeated soliton shapes, although it is concluded that this is merely a very accurate approximation and not a mathematical property of the model (as is often characteristic for cases of weak nonlinearity). By reducing the aforementioned model to its small amplitude counterpart (i.e. the Benjamin-Ono equation), an explanation is provided as to the fact that even for small wave amplitudes, there remains an apparent discrepancy between the models which increases as the period length shortens.