  We demonstrate that the fission of higher-order N-solitons with a subsequent
ejection of fundamental quasi-solitons creates solitonic cavities, formed by a
pair of solitons with dispersive light trapped between them. As a result of
multiple reflections of the trapped light from the bounding solitons which act
as mirrors, they bend their trajectories and collide. In the spectral-domain,
the two solitons receive blue and red wavelength shifts, respectively. The
spectrum of the bouncing trapped light alters as well. This phenomenon strongly
affect spectral characteristics of the generated supercontinuum. Studies of the
system's parameters, which are responsible for the creation of the cavities,
reveal possibilities of predicting and controlling soliton-soliton collisions
induced by multiple reflections of the trapped light.
