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

• Finite-genus solutions of the KdV equation are perturbed.
• These solutions are bounded on the real-axis and are physically relevant.
• Perturbations include dispersion and solitons.
• These perturbed solutions are computed numerically.
• No time stepping or spatial discretization is necessary.

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||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.