  The transformation of surface envelope solitons travelling over a bottom step
in water of a finite depth is studied. Using the transformation coefficients
earlier derived in the linear approximation, we find the parameters of
transmitted pulses and subsequent evolution of the pulses in the course of
propagation. Relying on the weakly nonlinear theory, the analytic formulae are
derived which describe the maximum attainable wave amplitude in the
neighbourhood of the step and in the far zone. Solitary waves may be greatly
amplified (within the weakly nonlinear theory - unrestrictedly much) when
propagate from relatively shallow water to the deeper domain due to the
constructive interference between the newly emerging envelope solitons and the
residual quasi-linear waves. The theoretical results are in a good agreement
with the data of direct numerical modelling of soliton transformation. In
particular, more than double wave amplification is demonstrated in the
performed simulations.
