  A long wave multi-dimensional approximation of shallow water waves is the
bi-directional Benney-Luke equation. It yields the well-known
Kadomtsev-Petviashvili equation in a quasi one-directional limit. A direct
perturbation method is developed; it uses the underlying conservation laws to
determine the slow evolution of parameters of two space dimensional,
non-decaying web-type solutions to the Benney-Luke equation. New numerical
simulations, based on windowing methods which are effective for non-decaying
data, are presented. These simulations support the analytical results and
elucidate the relationship between the Kadomtsev-Petviashvilli and the
Benney-Luke equations and are also used to obtain amplitude information
regarding particular web solutions. Additional dissipative perturbations to the
Benney-Luke equation are also studied.
