COMPUTATIONS OF BLOW-UP AND DECAY FOR PERIODIC-SOLUTIONS OF THE GENERALIZED KORTEWEG-DEVRIES-BURGERS EQUATION

A numerical scheme is suggested, discussed, and implemented for the approximation of solutions to the periodic initial-value problem for the generalized Korteweg-de Vries-Burgers equation. The resulting computer code is used to study singularity formation and other aspects of the interaction between nonlinearity, dispersion, and dissipation that is the hallmark of these evolutionary equations. It is found that unless the coefficient specifying the strength of the dissipation is large enough, initial data may lead to solutions that lose smoothness in finite time in exactly the same way as do solutions of the dissipationless equation.