  We provide a new analytical approach to operator splitting for equations of
the type $u_t=Au+B(u)$ where $A$ is a linear operator and $B$ is quadratic. A
particular example is the Korteweg-de Vries (KdV) equation $u_t-u
u_x+u_{xxx}=0$. We show that the Godunov and Strang splitting methods converge
with the expected rates if the initial data are sufficiently regular.
