The oscillations of a vertical column of stratified liquid with a free surface (Q1311566)

This is a continuation of the research reported in [\textit{S. A. Gobov}, \textit{B. B. Orazov} and \textit{A. G. Sveshnikov}, Zh. Vychisl. Mat. Mat. Fiz. 26, No. 8, 1223-1233 (1986; Zbl 0638.76026), Dokl. Akad. Nauk SSSR 295, 1041-1045 (1987; Zbl 0644.76117), \textit{S. A. Gabov} and \textit{A. G. Sveshnikov}, Linear problems of the theory of non-stationary internal waves (Nauka, Moskva 1990; Zbl 0713.76003)], involving the study of non- stationary internal waves in channels filled with a stratified liquid. We analyse the problem of nonstationary waves in a vertical channel of infinite depth with a free surface. An explicit solution is constructed and its behaviour over long periods of time is examined. The structure of normal non-stationary waves and effects due to the presence of the free surface are investigated.