Oblique interactions of weakly nonlinear long waves in dispersive systems

Masayuki Oikawa; Hidekazu Tsuji

doi:10.1016/j.fluiddyn.2006.07.002

Oblique interactions of weakly nonlinear long waves in dispersive systems

Masayuki Oikawa, Hidekazu Tsuji

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

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.

Original language	English
Pages (from-to)	868-898
Number of pages	31
Journal	Fluid Dynamics Research
Volume	38
Issue number	12
DOIs	https://doi.org/10.1016/j.fluiddyn.2006.07.002
Publication status	Published - Dec 1 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mechanical Engineering
Physics and Astronomy(all)
Fluid Flow and Transfer Processes

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10.1016/j.fluiddyn.2006.07.002

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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.",

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AU - Tsuji, Hidekazu

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AB - 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.

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JO - Fluid Dynamics Research

JF - Fluid Dynamics Research

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Oblique interactions of weakly nonlinear long waves in dispersive systems

Abstract

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