### Abstract

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

Pages (from-to) | 159-172 |

Number of pages | 14 |

Journal | Wave motion |

Volume | 0 |

Issue number | 15 |

DOIs | |

Publication status | Published - 1992 |

### Keywords

- METIS-140893
- IR-30253

### Cite this

*Wave motion*,

*0*(15), 159-172. https://doi.org/10.1016/0165-2125(92)90016-U

}

*Wave motion*, vol. 0, no. 15, pp. 159-172. https://doi.org/10.1016/0165-2125(92)90016-U

**Energy propagation in dissipative systems Part II: Centrovelocity for nonlinear wave equations.** / Derks, G.L.A.; Derks, G.; van Groesen, Embrecht W.C.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Energy propagation in dissipative systems Part II: Centrovelocity for nonlinear wave equations

AU - Derks, G.L.A.

AU - Derks, G.

AU - van Groesen, Embrecht W.C.

PY - 1992

Y1 - 1992

N2 - We consider nonlinear wave equations, first order in time, of a specific form. In the absence of dissipation, these equations are given by a Poisson system, with a Hamiltonian that is the integral of some density. The functional I, defined to be the integral of the square of the waveform, is a constant of motion of the unperturbed system. It will be shown that Z, the center of gravity of this density, is canonically conjugate to I and can be used as a measure to locate the position of the waveform. By introducing new coordinates based on Z, we get expressions for the centrovelocity, Image, and the decay of I, which compare to the ones of part I, in both the conservative and the dissipative case. With the derived expressions, we investigate the decay of solitary waves of the Korteweg-de Vries equation, when different kinds of dissipation are added.

AB - We consider nonlinear wave equations, first order in time, of a specific form. In the absence of dissipation, these equations are given by a Poisson system, with a Hamiltonian that is the integral of some density. The functional I, defined to be the integral of the square of the waveform, is a constant of motion of the unperturbed system. It will be shown that Z, the center of gravity of this density, is canonically conjugate to I and can be used as a measure to locate the position of the waveform. By introducing new coordinates based on Z, we get expressions for the centrovelocity, Image, and the decay of I, which compare to the ones of part I, in both the conservative and the dissipative case. With the derived expressions, we investigate the decay of solitary waves of the Korteweg-de Vries equation, when different kinds of dissipation are added.

KW - METIS-140893

KW - IR-30253

U2 - 10.1016/0165-2125(92)90016-U

DO - 10.1016/0165-2125(92)90016-U

M3 - Article

VL - 0

SP - 159

EP - 172

JO - Wave motion

JF - Wave motion

SN - 0165-2125

IS - 15

ER -