On the evolution of perturbations to solutions of the Kadomtsev–Petviashvilli equation using the Benney–Luke equation

Abstract

The Benney–Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev–Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney–Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney–Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.