Abstract
In Sec. 1 the stability of small-amplitude steady-state periodic solutions of Eq. (0.1) in the neighborhood of k=kn are investigated. The results of the investigations are consistent with those of [1]. In Sec. 2 the stability of periodic waves not lying in the neighborhood of resonance is considered. It is shown that in the region of instability when α=1 steady-state solutions of the soliton type with oscillatory structure may exist. In Sec. 3 the properties of certain exact solutions — periodic waves and solitons — are studied in relation to the nature of the singular points of the dynamical system derived from (0.1). In Sec. 4 the evolution of rapidly decreasing Cauchy data is considered.
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 88–95, January–February, 1989.
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Il'ichev, A.T., Marchenko, A.V. Propagation of long nonlinear waves in a ponderable fluid beneath an ice sheet. Fluid Dyn 24, 73–79 (1989). https://doi.org/10.1007/BF01051481
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DOI: https://doi.org/10.1007/BF01051481