### Abstract

It is shown that the simplest two-dimensional long wave nonlinear model for the propagation of the rogue waves corresponds to the Kadomtsev-Petviashvili (KP) equation. The mechanism of the rogue wave formation is suggested based on a resonant head-on collision of two plane incidentally non-interacting waves. Corresponding numerical solution of the KP equation is obtained to account for the formation of localized abnormally high amplitude wave. Peculiarities of the solution allows to explain rare but unexpected appearance of the rogue waves. The shape of the steady state of the solution differs from that of the exact two-soliton solution of the KP equation.

Original language | English |
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Title of host publication | Proceedings of the International Seminar - Days on Diffraction 2004 |

Editors | I.V. Andronov |

Pages | 154-162 |

Number of pages | 9 |

Publication status | Published - Dec 1 2004 |

Event | International Seminar - Days on Diffraction 2004 - St. Petersburg, Russian Federation Duration: Jun 29 2004 → Jul 2 2004 |

### Publication series

Name | Proceedings of the International Seminar - Days on Diffraction 2004 |
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### Other

Other | International Seminar - Days on Diffraction 2004 |
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Country | Russian Federation |

City | St. Petersburg |

Period | 6/29/04 → 7/2/04 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Proceedings of the International Seminar - Days on Diffraction 2004*(pp. 154-162). (Proceedings of the International Seminar - Days on Diffraction 2004).

**Formation of abnormally high localized waves due to nonlinear two-dimensional waves interaction.** / Porubov, A. V.; Lavrenov, I. V.; Tsuji, H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the International Seminar - Days on Diffraction 2004.*Proceedings of the International Seminar - Days on Diffraction 2004, pp. 154-162, International Seminar - Days on Diffraction 2004, St. Petersburg, Russian Federation, 6/29/04.

}

TY - GEN

T1 - Formation of abnormally high localized waves due to nonlinear two-dimensional waves interaction

AU - Porubov, A. V.

AU - Lavrenov, I. V.

AU - Tsuji, H.

PY - 2004/12/1

Y1 - 2004/12/1

N2 - It is shown that the simplest two-dimensional long wave nonlinear model for the propagation of the rogue waves corresponds to the Kadomtsev-Petviashvili (KP) equation. The mechanism of the rogue wave formation is suggested based on a resonant head-on collision of two plane incidentally non-interacting waves. Corresponding numerical solution of the KP equation is obtained to account for the formation of localized abnormally high amplitude wave. Peculiarities of the solution allows to explain rare but unexpected appearance of the rogue waves. The shape of the steady state of the solution differs from that of the exact two-soliton solution of the KP equation.

AB - It is shown that the simplest two-dimensional long wave nonlinear model for the propagation of the rogue waves corresponds to the Kadomtsev-Petviashvili (KP) equation. The mechanism of the rogue wave formation is suggested based on a resonant head-on collision of two plane incidentally non-interacting waves. Corresponding numerical solution of the KP equation is obtained to account for the formation of localized abnormally high amplitude wave. Peculiarities of the solution allows to explain rare but unexpected appearance of the rogue waves. The shape of the steady state of the solution differs from that of the exact two-soliton solution of the KP equation.

UR - http://www.scopus.com/inward/record.url?scp=29144492153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29144492153&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:29144492153

SN - 5965100647

SN - 9785965100644

T3 - Proceedings of the International Seminar - Days on Diffraction 2004

SP - 154

EP - 162

BT - Proceedings of the International Seminar - Days on Diffraction 2004

A2 - Andronov, I.V.

ER -