  We consider the dynamics of internal envelope solitons in a two-layer
rotating fluid with a linearly varying bottom. It is shown that the most
probable frequency of a carrier wave which constitutes the solitary wave is the
frequency where the growth rate of modulation instability is maximal. An
envelope solitary wave of this frequency can be described by the conventional
nonlinear Schrodinger equation. A soliton solution to this equation is
presented for the time-like version of the nonlinear Schrodinger equation. When
such envelope soliton enters a coastal zone where the bottom gradually linearly
increases, then it experiences an adiabatical transformation. This leads to an
increase of soliton amplitude, velocity, and period of a carrier wave, whereas
its duration decreases. It is shown that the soliton becomes taller and
narrower. At some distance it looks like a breather, a narrow nonstationary
solitary wave. The dependences of soliton parameters on the distance when it
moves towards the shoaling are found from the conservation laws and analysed
graphically. Estimates for the real ocean are presented.
