### Abstract

A bifurcation problem for steady surface waves over a periodic bottom is studied. It is assumed that the motion of the fluid is symmetric with respect to a vertical axis and periodic in the horizontal direction. In the case of flat bottom, we have infinitely many bifurcations from the trivial uniform flow. All of them are the pitchfork bifurcation and occur subcritically. If the bottom is not flat but close to flat, then the corresponding bifurcation equation is subject to a small perturbation. Since we know a universal unfolding of the pitchfork, the bifurcation diagram must be equivalent to one of several particular patterns. We will give relations between the patterns and functions representing the bottom, that is, we will specify which pattern is realised.

Original language | English |
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Pages (from-to) | 219-239 |

Number of pages | 21 |

Journal | Wave Motion |

Volume | 37 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2003 Mar |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics

### Cite this

**On steady surface waves over a periodic bottom : Relations between the pattern of imperfect bifurcation and the shape of the bottom.** / Iguchi, Tatsuo.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On steady surface waves over a periodic bottom

T2 - Relations between the pattern of imperfect bifurcation and the shape of the bottom

AU - Iguchi, Tatsuo

PY - 2003/3

Y1 - 2003/3

N2 - A bifurcation problem for steady surface waves over a periodic bottom is studied. It is assumed that the motion of the fluid is symmetric with respect to a vertical axis and periodic in the horizontal direction. In the case of flat bottom, we have infinitely many bifurcations from the trivial uniform flow. All of them are the pitchfork bifurcation and occur subcritically. If the bottom is not flat but close to flat, then the corresponding bifurcation equation is subject to a small perturbation. Since we know a universal unfolding of the pitchfork, the bifurcation diagram must be equivalent to one of several particular patterns. We will give relations between the patterns and functions representing the bottom, that is, we will specify which pattern is realised.

AB - A bifurcation problem for steady surface waves over a periodic bottom is studied. It is assumed that the motion of the fluid is symmetric with respect to a vertical axis and periodic in the horizontal direction. In the case of flat bottom, we have infinitely many bifurcations from the trivial uniform flow. All of them are the pitchfork bifurcation and occur subcritically. If the bottom is not flat but close to flat, then the corresponding bifurcation equation is subject to a small perturbation. Since we know a universal unfolding of the pitchfork, the bifurcation diagram must be equivalent to one of several particular patterns. We will give relations between the patterns and functions representing the bottom, that is, we will specify which pattern is realised.

UR - http://www.scopus.com/inward/record.url?scp=0037369325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037369325&partnerID=8YFLogxK

U2 - 10.1016/S0165-2125(02)00075-6

DO - 10.1016/S0165-2125(02)00075-6

M3 - Article

AN - SCOPUS:0037369325

VL - 37

SP - 219

EP - 239

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

IS - 3

ER -