We demonstrate experimentally the existence of a family of
gravity-induced finiteamplitude water waves that propagate
practically without change of form in shallow water of uniform
depth. The surface patterns of these waves are genuinely
two-dimensional, and periodic. The basic template of a wave is
hexagonal, but it need not be symmetric about the direction of
propagation, as required in our previous studies (e.g. Hammack
et al. 1989). Like the symmetric waves in
earlier studies, the asymmetric waves studied here are easy to
generate, they seem to be stable to perturbations, and their
amplitudes need not be small. The Kadomtsev–Petviashvili (KP)
equation is known to describe approximately the evolution of waves
in shallow water, and an eight-parameter family of exact solutions
of this equation ought to describe almost all spatially periodic
waves of permanent form. We present an algorithm to obtain the eight
parameters from wave-gauge measurements. The resulting KP solutions
are observed to describe the measured waves with reasonable
accuracy, even outside the putative range of validity of the KP
model.