The Korteweg-de Vries-Burgers equation

Abstract The time evolution and stability of the shock solutions of the Korteweg-de Vries-Burgers equation are studied numerically. It is found that nonanalytic initial data satisfying the boundary conditions of the problem evolve asymptotically into the steady-state shocks predicted by a time-independent analysis. Like Burgers' equation, the Korteweg-de Vries-Burgers equation has a unique shock profile; this analogy suggests that the Kortewegde Vries-Burgers shocks are stable against small perturbations, while the numerical experiments suggest further that the shocks are stable even when subject to large perturbations.