The generation and evolution of lump solitary waves in surface-tension-dominated flows

Three-dimensional solitary waves or lump solitons are known to be solutions to the Kadomtsev Petviashvili equation, which models small-amplitude shallow-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-Luke equation with surface tension. Here we establish an explicit connection between the lump solitons of these two equations and numerically compute the Benney-Luke lump solitons and their speed-amplitude relation. Furthermore, 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 are periodically generated.