Oblique interactions of weakly nonlinear long waves in dispersive systems

Oblique interactions of weakly nonlinear long waves in dispersive systems

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 extende...

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Veröffentlicht in:Fluid dynamics research 2006-12, Vol.38 (12), p.868-898
Hauptverfasser: Oikawa, Masayuki, Tsuji, Hidekazu
Format: Artikel
Sprache:eng
Schlagworte:
Kadomtsev–Petviashvili equation
Mach reflection
Nonlinear wave propagation
Oblique interaction
Solitary waves
Soliton
Soliton resonance
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Zusammenfassung: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.
ISSN:0169-5983
1873-7005
1873-7005
DOI:10.1016/j.fluiddyn.2006.07.002