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Numerical study of the KP equation for non-periodic waves

Author

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  • Kao, Chiu-Yen
  • Kodama, Yuji

Abstract

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 paper. The classification is based on the far-field patterns of the solutions which consist of a finite number of line-solitons. In this paper, we study the initial value problem of the KP equation with V- and X-shape initial waves consisting of two distinct line-solitons by means of the direct numerical simulation. 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 paper are related to the rogue waves generated by nonlinear wave interactions in shallow water wave problem.

Suggested Citation

  • Kao, Chiu-Yen & Kodama, Yuji, 2012. "Numerical study of the KP equation for non-periodic waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(7), pages 1185-1218.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:7:p:1185-1218
    DOI: 10.1016/j.matcom.2010.05.025
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