  All solutions of the Korteweg -- de Vries equation that are bounded on the
real line are physically relevant, depending on the application area of
interest. Usually, both analytical and numerical approaches consider solution
profiles that are either spatially localized or (quasi)periodic. In this paper,
we discuss a class of solutions that is a nonlinear superposition of these two
cases: their asymptotic state for large $|x|$ is (quasi)periodic, but they may
contain solitons, with or without dispersive tails. Such scenarios might occur
in the case of localized perturbations of previously present sea swell, for
instance. Such solutions have been discussed from an analytical point of view
only recently. We numerically demonstrate different features of these
solutions.
