The new soliton solutions of the model of semi-bounded ferrimagnet with two crystallographycally different magnetic sublattices are found and analyzed in the exchange approximation. The boundary conditions for free surface spins on the edge of the sample are taken into account. It is established, that the localization of solitons near the boundary of the sample is impossible at such conditions. During the collision of the moving solitons with the edge of the sample their cores undergo significant changes, which are accompanied by remagnetization of the medium near the sample surface. After the reflection of solitons from the surface, when moving inside the sample, the soliton cores acquire the stationary form, typical for the precessing solitons of the unbounded medium. The changes of the internal precession phases and shifts of the soliton centers after the reflection from the sample boundary are calculated. Keywords: solitons, Landau-Lifshitz equation, ferrimagnets.
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