Operator splitting methods for generalized Korteweg-de Vries equations

We apply the method of operator splitting on the generalized Korteweg-de Vr ies (KdV) equation u(t) + f(u)(x) + epsilon u(xxx) = 0, by solving the nonl inear conservation law u(t) + f(u)(x) = 0 and the linear dispersive equatio n u(t) + epsilon u(xxx) = 0 sequentially. We prove that if the approximatio n obtained by operator splitting converges, then the limit function is a we ak solution of the generalized KdV equation. Convergence properties are ana lyzed numerically by studying the effect of combining different numerical m ethods for each of the simplified problems. (C) 1999 Academic Press.