### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 507-516 |

Journal | Acta applicandae mathematicae |

Volume | 39 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1995 |

### Keywords

- IR-50303

### Cite this

*Acta applicandae mathematicae*,

*39*(1-3), 507-516. https://doi.org/10.1007/BF00994652

}

*Acta applicandae mathematicae*, vol. 39, no. 1-3, pp. 507-516. https://doi.org/10.1007/BF00994652

**Evolving solitons in bubbly flows.** / van Wijngaarden, L.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - Evolving solitons in bubbly flows

AU - van Wijngaarden, L.

PY - 1995

Y1 - 1995

N2 - At the end of the sixties, it was shown that pressure waves in a bubbly liquid obey the KdV equation, the nonlinear term coming from convective acceleration and the dispersive term from volume oscillations of the bubbles. For a variableu, proportional to –p, wherep denotes pressure, the appropriate KdV equation can be casted in the formu t –6uu x +u xxx =0. The theory of this equation predicts that, under certain conditions, solitons evolve from an initial profileu(x,0). In particular, it can be shown that the numberN of those solitons can be found from solving the eigenvalue problem xx–u(x,0)=0, with(0)=1 and(0)=0.N is found from counting the zeros of the solution of this equation betweenx=0 andx=Q, say,Q being determined by the shape ofu(x,0). We took as an initial pressure profile a Shockwave, followed by an expansion wave. This can be realised in the laboratory and the problem, formulated above, can be solved exactly. In this contribution the solution is outlined and it is shown from the experimental results that from the said initial disturbance, indeed solitons evolve in the predicated quantity.

AB - At the end of the sixties, it was shown that pressure waves in a bubbly liquid obey the KdV equation, the nonlinear term coming from convective acceleration and the dispersive term from volume oscillations of the bubbles. For a variableu, proportional to –p, wherep denotes pressure, the appropriate KdV equation can be casted in the formu t –6uu x +u xxx =0. The theory of this equation predicts that, under certain conditions, solitons evolve from an initial profileu(x,0). In particular, it can be shown that the numberN of those solitons can be found from solving the eigenvalue problem xx–u(x,0)=0, with(0)=1 and(0)=0.N is found from counting the zeros of the solution of this equation betweenx=0 andx=Q, say,Q being determined by the shape ofu(x,0). We took as an initial pressure profile a Shockwave, followed by an expansion wave. This can be realised in the laboratory and the problem, formulated above, can be solved exactly. In this contribution the solution is outlined and it is shown from the experimental results that from the said initial disturbance, indeed solitons evolve in the predicated quantity.

KW - IR-50303

U2 - 10.1007/BF00994652

DO - 10.1007/BF00994652

M3 - Article

VL - 39

SP - 507

EP - 516

JO - Acta applicandae mathematicae

JF - Acta applicandae mathematicae

SN - 0167-8019

IS - 1-3

ER -