Km. Berger et Pa. Milewski, The generation and evolution of lump solitary waves in surface-tension-dominated flows, SIAM J A MA, 61(3), 2000, pp. 731-750
Three-dimensional solitary waves or lump solitons are known to be solutions
to the Kadomtsev Petviashvili equation, which models small-amplitude shall
ow-water waves when the Bond number is greater than 1/3. Recently, Pego and
Quintero presented a proof of the existence of such waves for the Benney-L
uke equation with surface tension. Here we establish an explicit connection
between the lump solitons of these two equations and numerically compute t
he Benney-Luke lump solitons and their speed-amplitude relation. Furthermor
e, we numerically collide two Benney-Luke lump solitons to illustrate their
soliton wave character. Finally, we study the ow over an obstacle near the
linear shallow-water speed and show that three-dimensional lump solitons a
re periodically generated.