### Abstract

This Brief Communication answers an unsettled question pointed out by Peters and Stoker [Commun. Pure Appl. Math 13, 115 (1960)] with regard to a critical case of a two-layer fluid flow with a free surface supported by a horizontal rigid bottom. In the critical case the coefficient of the nonlinear term in the Korteweg-deVries (KdV) equation vanishes and the KdV theory models only a parallel flow. By using higher-order asymptotic expansion, an extended and a modified KdV equation are derived and internal solitary waves and transition waves in the critical case are found.

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

Pages (from-to) | 2804-2806 |

Number of pages | 3 |

Journal | Physics of Fluids |

Volume | 9 |

Issue number | 9 |

Publication status | Published - 1997 Sep 1 |

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### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*9*(9), 2804-2806.

**On a critical case of internal solitary waves in a two-layer fluid.** / Choi, Jeongwhan; Shen, M. C.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 9, no. 9, pp. 2804-2806.

}

TY - JOUR

T1 - On a critical case of internal solitary waves in a two-layer fluid

AU - Choi, Jeongwhan

AU - Shen, M. C.

PY - 1997/9/1

Y1 - 1997/9/1

N2 - This Brief Communication answers an unsettled question pointed out by Peters and Stoker [Commun. Pure Appl. Math 13, 115 (1960)] with regard to a critical case of a two-layer fluid flow with a free surface supported by a horizontal rigid bottom. In the critical case the coefficient of the nonlinear term in the Korteweg-deVries (KdV) equation vanishes and the KdV theory models only a parallel flow. By using higher-order asymptotic expansion, an extended and a modified KdV equation are derived and internal solitary waves and transition waves in the critical case are found.

AB - This Brief Communication answers an unsettled question pointed out by Peters and Stoker [Commun. Pure Appl. Math 13, 115 (1960)] with regard to a critical case of a two-layer fluid flow with a free surface supported by a horizontal rigid bottom. In the critical case the coefficient of the nonlinear term in the Korteweg-deVries (KdV) equation vanishes and the KdV theory models only a parallel flow. By using higher-order asymptotic expansion, an extended and a modified KdV equation are derived and internal solitary waves and transition waves in the critical case are found.

UR - http://www.scopus.com/inward/record.url?scp=0030725303&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030725303&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 2804

EP - 2806

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 9

ER -