  One-parameter families of exact two-component solitary-wave solutions for
interacting high-frequency (HF) and low-frequency (LF) waves are found in the
framework of Zakharov-type models, which couple the nonlinear Schr\"odinger
equation (NLSE) for intense HF waves to the Boussinesq (Bq) or Korteweg - de
Vries (KdV) equation for the LF component through quadratic terms. The systems
apply, in particular, to the interaction of surface (HF) and internal (LF)
waves in stratified fluids. These solutions are two-component generalizations
of the single-component Bq and KdV solitons. Perturbed dynamics and stability
of the solitary waves are studied in detail by means of analytical and
numerical methods. Essentially, they are stable against separation of the HF
and LF components if the latter one is shaped as a potential well acting on the
HF field, and unstable, against splitting of the two components, with a
barrier-shaped LF one. Collisions between the solitary waves are studied by
means of direct simulations, demonstrating a trend to merger of in-phase
solitons, and elastic interactions of out-of-phase ones.
