A Riemann-Hilbert problem for the finite-genus solutions of the KdV equation and its numerical solution

► A new Riemann-Hilbert problem for the finite-genus solutions of the Korteweg-de Vries equation is derived.► These finite-genus solutions are computed numerically. ► No time stepping or spatial discretization is necessary. ► The approximation is seen to be uniformly valid for all space and time.