Abstract:

 A fluid layer of finite depth is described by Euler's equations governing the motions of the ideal fluid (water). The ice  is assumed to be solid and it freely floats on the water surface. The ice cover is modeled by a geometrically  non-linear elastic Kirchhoff-Love plate. The trajectories of liquid particles under the ice cover are found in the field of different nonlinear surface traveling waves of small, but finite amplitude. These waves are: the classical solitary wave of depression, existing on the water-ice interface when the initial stress in the ice cover is large enough, the  generalized solitary wave, the envelope solitary wave and the so-called dark soliton. The last two waves indicate the focusing or defocusing of nonlinear carier  surface wave, the generalized solitary wave consists of solitary wave core and periodic asymptotic wave at spacial infinity, moreover for the algebraically small amplitude of the wave core the amplitude of the mentioned above periodic wave is exponentially small. The consideration is based on explicit asymptotic expressions for solutions describing  the mentioned wave structures on the water-ice interface, as well as asymptotic solutions for the velocity field in the liquid column corresponding to these waves.