Adiabatic decay of internal solitons due to Earth's rotation within the framework of the Gardner-Ostrovsky equation.

The adiabatic decay of different types of internal wave solitons caused by the Earth's rotation is studied within the framework of the Gardner-Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions: (u + c u + α u u + α u u + β u) = γ u. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth's rotation described by the parameter γ. The characteristic decay time is derived for different types of solitons for positive and negative coefficients of cubic nonlinearity α (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity α determines only a polarity of solitary wave when α < 0 or the asymmetry of solitary waves of opposite polarity when α > 0. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when α is negative, are structurally unstable. Under the influence of Earth's rotation, they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.