  We study solitary wave solutions of the fifth-order Korteweg - de Vries
equation which contains, besides the traditional quadratic nonlinearity and
third-order dispersion, additional terms including cubic nonlinearity and fifth
order linear dispersion, as well as two nonlinear dispersive terms. An exact
solitary wave solution to this equation is derived and the dependence of its
amplitude, width and speed on the parameters of the governing equation are
studied. It is shown that the derived solution can represent either an embedded
or regular soliton depending on the equation parameters. The nonlinear
dispersive terms can drastically influence the existence of solitary waves,
their nature (regular or embedded), profile, polarity, and stability with
respect to small perturbations. We show, in particular, that in some cases
embedded solitons can be stable even with respect to interactions with regular
solitons. The results obtained are applicable to surface and internal waves in
fluids, as well as to waves in other media (plasma, solid waveguides, elastic
media with microstructure, etc.).
