Nonlinear-dispersive model for surface wave transformation in coastal zone of ice coated see (Q2755199)

The long-wave nonlinear-dispersive model for propagation of bending-gravity waves in an elastic plate floating on the surface of variable-depth fluid is constructed. The model takes into account effects of nonlinear dispersion and inertia, elasticity and geometrically nonlinear deflection of plate. On the basis of this model, an hierarchical sequence of simpler models is developed. These models generalize known in the water wave theory models of Peregrin, Boussinesq and Korteweg-de Vries to the case of the bending-gravity waves. In a particular case of extended KdV-equation an exact solution has been obtained which describes the properties of solitary and cnoidal waves in the sea covered by broken and unbroken ice. It is shown that the bending-gravity waves are characterized by some features in comparison with the nonlinear long water waves, i.e. unlike the usual solution the cavity propagates without change of the form. The velocity of propagation of bending-gravity waves decreases with increasing amplitude. Moreover, the characteristics of the bending-gravity waves are determined by amplitude and dispersion due to bending rigidity of a plate, and do not depend on water dispersion and inertial properties of ice cover.