### Abstract

We illustrate the behaviour of a system of nonlinear dispersive PDEs modelling the propagation of water waves in a finite space interval, by comparing it with the behaviour of the corresponding linearized PDE system. We review how in general the interaction with the boundary destroys the nonlinear effects, reducing the evolution to an essentially linear dispersive phenomenon. In one particular case of homogeneous boundary conditions, it has been observed numerically that the evolution and in particular the solitary waves generated from the initial waveform persist beyond the interaction with the boundary, which is in this sense transparent. We show how in this case the solution of the linearized problem has a specific structure and propose that this can be used as a characterizing property of those boundary conditions that lead to “transparent” boundaries.

Original language | English |
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Title of host publication | Nonlinear Physics |

Subtitle of host publication | Theory and Experiment II |

Editors | M. J. Ablowitz, M. Boiti, F. Pempinelli |

Publisher | World Scientific Publishing |

Pages | 287-294 |

Number of pages | 8 |

ISBN (Electronic) | 9789814486699 |

ISBN (Print) | 9789812382702 |

DOIs | |

Publication status | Published - Apr 2003 |

Event | International workshop on nonlinear phenomena 2002 - Gallipoli, Italy Duration: 27 Jun 2002 → 6 Jul 2002 |

### Conference

Conference | International workshop on nonlinear phenomena 2002 |
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Country | Italy |

City | Gallipoli |

Period | 27/06/02 → 6/07/02 |

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## Cite this

Pelloni, B. (2003). Linear and nonlinear waves on a finite interval. In M. J. Ablowitz, M. Boiti, & F. Pempinelli (Eds.),

*Nonlinear Physics: Theory and Experiment II*(pp. 287-294). World Scientific Publishing. https://doi.org/10.1142/9789812704467_0041