### Abstract

Two-dimensional (2D) interactions of two interfacial solitons in a two-layer fluid of finite depth are investigated under the assumption of a small but finite amplitude. When the angle v between the wave normals of two solitons is not small, it is shown by a perturbation method that in the lowest order of approximation the solution is a superposition of two intermediate long wave (ILW) solitons and in the next order of approximation the effect of the interaction appears as position phase shifts and as an increase in amplitude at the interaction center of two solitons. When v is small, it is shown that the interaction is described approximately by a nonlinear integro-partial differential equation that we call the two-dimensional ILW (2DILW) equation. By solving it numerically for a V-shaped initial wave that is an appropriate initial value for the oblique reflection of a soliton due to a rigid wall, it is shown that for a relatively large angle of incidence v_{i} the reflection is regular, but for a relatively small v_{i} the reflection is not regular and a new wave called stem is generated. The results are also compared with those of the Kadomtsev-Petviashvili (KP) equation and of the two-dimensional Benjamin-Ono (2DBO) equation.

Original language | English |
---|---|

Article number | 065506 |

Journal | Fluid Dynamics Research |

Volume | 42 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 1 2010 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Fluid Dynamics Research*,

*42*(6), [065506]. https://doi.org/10.1088/0169-5983/42/6/065506

**Two-dimensional interactions of solitons in a two-layer fluid of finite depth.** / Tsuji, Hidekazu; Oikawa, Masayuki.

Research output: Contribution to journal › Article

*Fluid Dynamics Research*, vol. 42, no. 6, 065506. https://doi.org/10.1088/0169-5983/42/6/065506

}

TY - JOUR

T1 - Two-dimensional interactions of solitons in a two-layer fluid of finite depth

AU - Tsuji, Hidekazu

AU - Oikawa, Masayuki

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Two-dimensional (2D) interactions of two interfacial solitons in a two-layer fluid of finite depth are investigated under the assumption of a small but finite amplitude. When the angle v between the wave normals of two solitons is not small, it is shown by a perturbation method that in the lowest order of approximation the solution is a superposition of two intermediate long wave (ILW) solitons and in the next order of approximation the effect of the interaction appears as position phase shifts and as an increase in amplitude at the interaction center of two solitons. When v is small, it is shown that the interaction is described approximately by a nonlinear integro-partial differential equation that we call the two-dimensional ILW (2DILW) equation. By solving it numerically for a V-shaped initial wave that is an appropriate initial value for the oblique reflection of a soliton due to a rigid wall, it is shown that for a relatively large angle of incidence vi the reflection is regular, but for a relatively small vi the reflection is not regular and a new wave called stem is generated. The results are also compared with those of the Kadomtsev-Petviashvili (KP) equation and of the two-dimensional Benjamin-Ono (2DBO) equation.

AB - Two-dimensional (2D) interactions of two interfacial solitons in a two-layer fluid of finite depth are investigated under the assumption of a small but finite amplitude. When the angle v between the wave normals of two solitons is not small, it is shown by a perturbation method that in the lowest order of approximation the solution is a superposition of two intermediate long wave (ILW) solitons and in the next order of approximation the effect of the interaction appears as position phase shifts and as an increase in amplitude at the interaction center of two solitons. When v is small, it is shown that the interaction is described approximately by a nonlinear integro-partial differential equation that we call the two-dimensional ILW (2DILW) equation. By solving it numerically for a V-shaped initial wave that is an appropriate initial value for the oblique reflection of a soliton due to a rigid wall, it is shown that for a relatively large angle of incidence vi the reflection is regular, but for a relatively small vi the reflection is not regular and a new wave called stem is generated. The results are also compared with those of the Kadomtsev-Petviashvili (KP) equation and of the two-dimensional Benjamin-Ono (2DBO) equation.

UR - http://www.scopus.com/inward/record.url?scp=78349287315&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78349287315&partnerID=8YFLogxK

U2 - 10.1088/0169-5983/42/6/065506

DO - 10.1088/0169-5983/42/6/065506

M3 - Article

VL - 42

JO - Fluid Dynamics Research

JF - Fluid Dynamics Research

SN - 0169-5983

IS - 6

M1 - 065506

ER -