  The dynamics of two-component solitons with a small spatial displacement of
the high-frequency (HF) component relative to the low-frequency (LF) one is
investigated in the framework of the Zakharov-type system. In this system, the
evolution of the HF field is governed by a linear Schr\"odinger equation with
the potential generated by the LF field, while the LF field is governed by a
Korteweg-de Vries (KdV) equation with an arbitrary dispersion-nonlinearity
ratio and a quadratic term accounting for the HF feedback on the LF field. The
oscillation frequency of the soliton's HF component relative to the LF one is
found analytically. It is shown that the solitons are stable against small
perturbations. The analytical results are confirmed by numerical simulations.
