The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and classified. Those soliton solutions are localized along certain lines in a two-dimensional plane and decay exponentially everywhere else, and they are called line-soliton solutions. In this talk, we will present the study of the initial value problem of the KP equation with V- and X-shape initial waves consisting of two distinct line-solitons by means of direct numerical simulations. We then show that the solution converges asymptotically to some of those exact soliton solutions. The convergence is in a locally defined L2-sense. The initial wave patterns considered in this talk are related to the rogue waves generated by nonlinear wave interactions in the shallow water wave problem.
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