  This paper treats nonlinear wave current interactions in their simplest form,
as an overtaking collision. In one spatial dimension, the paper investigates
the collision interaction formulated as an initial value problem of a Burgers
bore overtaking solutions of two types of nonlinear wave equations, Korteweg de
Vries (KdV) and nonlinear Schrodinger (NLS). The bore wave state arising after
the overtaking Burgers-KdV collision in numerical simulations is found to
depend qualitatively on the balance between nonlinearity and dispersion in the
KdV equation. The Burgers-KdV system is also made stochastic by following the
stochastic advection by Lie transport approach (SALT).
