The nonlinear long waves generated by a disturbance moving at subcritical, critical
and supercritical speed in unbounded shallow water are investigated. The problem is
formulated by a new modified generalized Boussinesq equation and solved numerically
by an implicit finite-difference algorithm. Three-dimensional upstream solitary waves
with significant amplitude are generated with a periodicity by a pressure distribution
or slender strut advancing on the free surface. The crestlines of these solitons are
almost perfect parabolas with decreasing curvature with respect to time. Behind the
disturbance, a complicated, divergent Kelvin-like wave pattern is formed. It is found
that, unlike the wave breaking phenomena in a narrow channel at Fh [ges ] 1.2, the three-
dimensional upstream solitons form several parabolic water humps and are blocked
ahead of the disturbance at supercritical speed in an unbounded domain for large
time.