Soliton interactions of the Kadomtsev-Petviashvili equation and generation of large-amplitude water waves. (English) Zbl 1172.35475
Stud. Appl. Math. 122, No. 4, 377-394 (2009); corrigendum ibid. 123, No. 4, 375-376 (2009).
Summary: We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of KPII. We also describe a method to predict the possible maximum wave amplitude from asymptotic data. Finally, we report on numerical simulations of multi-soliton complexes of the KPII equation which verify the robustness of all types of soliton interactions and web-like structure.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35Q51 | Soliton equations |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
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