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All solutions of the Korteweg -- de Vries equation that are bounded on thereal line are physically relevant, depending on the application area ofinterest. Usually, both analytical and numerical approaches consider solutionprofiles that are either spatially localized or (quasi)periodic. In this paper,we discuss a class of solutions that is a nonlinear superposition of these twocases: their asymptotic state for large $|x|$ is (quasi)periodic, but they maycontain solitons, with or without dispersive tails. Such scenarios might occurin the case of localized perturbations of previously present sea swell, forinstance. Such solutions have been discussed from an analytical point of viewonly recently. We numerically demonstrate different features of thesesolutions.

Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: computational results