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Oblique interactions of weakly nonlinear long waves in dispersive systems |
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| Authors: | Masayuki Oikawa Hidekazu Tsuji |
| Affiliation: | aResearch Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-koen, Kasuga-shi, Fukuoka-ken 816-8580, Japan |
| Abstract: | Studies on the oblique interactions of weakly nonlinear long waves in dispersive systems are surveyed. We focus mainly our concentration on the two-dimensional interaction between solitary waves. Two-dimensional Benjamin–Ono (2DBO) equation, modified Kadomtsev–Petviashvili (MKP) equation and extended Kadomtsev–Petviashvili (EKP) equation as well as the Kadomtsev–Petviashvili (KP) equation are treated. It turns out that a large-amplitude wave can be generated due to the oblique interaction of two identical solitary waves in the 2DBO and the MKP equations as well as in the KP-II equation. Recent studies on exact solutions of the KP equation are also surveyed briefly. |
| Keywords: | Solitary waves Soliton Kadomtsev–Petviashvili equation Oblique interaction Mach reflection Soliton resonance Nonlinear wave propagation |
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