### Abstract

In numerical and physical experiments it is often observed that finite and infinite dimensional systems exhibit a low dimensional behaviour, in the sense that the dynamics looks as if it can be described with a few parameters. Often a spatially coherent structure is characteristic for the phenomenon. A well known example is a solitary wave, characterized by its phase and its amplitude. In this paper we consider a Hamiltonian system (or a Poisson system), that has an additional constant of motion (besides the Hamiltonian). We show coherent structures in such a system, by describing some solutions with 2 parameters, induced by the constant of motion. Further we demonstrate that the coherent structures survive even in cases where a small perturbation, such as dissipation, is present. This is demonstrated in some detail for a spherical pendulum with uniform friction, for the Korteweg-de Vries equation with uniform damping and for the Korteweg-de Vries-Burgers equation.

Original language | English |
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Title of host publication | Integration of Theory and Applications in Applied Mechanics |

Subtitle of host publication | Choice of papers presented at the First National Mechanics Congress, April 2–4, 1990, Rolduc, Kerkrade, The Netherlands |

Editors | J.F. Dijksman, F.T.M. Nieuwstadt |

Place of Publication | Dordrecht |

Publisher | Kluwer Academic Publishers |

Pages | 329-340 |

Number of pages | 11 |

ISBN (Electronic) | 978-94-009-2125-2 |

ISBN (Print) | 978-94-010-7456-8 |

DOIs | |

Publication status | Published - 1990 |

Event | 1st National Mechanics Congress 1990 - Rolduc, Kerkrade, Netherlands Duration: 2 Apr 1990 → 4 Apr 1990 Conference number: 1 |

### Conference

Conference | 1st National Mechanics Congress 1990 |
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Country | Netherlands |

City | Rolduc, Kerkrade |

Period | 2/04/90 → 4/04/90 |

### Keywords

- Solitary wave
- Hamiltonian systems
- Coherent structures
- Relative equilibrium
- Additional constant

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## Cite this

Derks, G., van Groesen, E., & Valkering, T. (1990). Decay of coherent structures in damped Hamiltonian systems. In J. F. Dijksman, & F. T. M. Nieuwstadt (Eds.),

*Integration of Theory and Applications in Applied Mechanics: Choice of papers presented at the First National Mechanics Congress, April 2–4, 1990, Rolduc, Kerkrade, The Netherlands*(pp. 329-340). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/978-94-009-2125-2_24