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In this paper we present the unification of two existing numerical methodsfor the construction of solutions of the Korteweg-de Vries (KdV) equation. Thefirst method is used to solve the Cauchy initial-value problem on the line forrapidly decaying initial data. The second method is used to computefinite-genus solutions of the KdV equation. The combination of these numericalmethods allows for the computation of exact solutions that are asymptotically(quasi-)periodic finite-gap solutions and are a nonlinear superposition ofdispersive, soliton and (quasi-)periodic solutions in the finite (x,t)-plane.Such solutions are referred to as superposition solutions. We compute thesesolutions accurately for all values of x and t.

A numerical dressing method for the nonlinear superposition of solutions of the KdV equation