Linear and nonlinear waves on a finite interval

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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 languageEnglish
Title of host publicationNonlinear Physics
Subtitle of host publicationTheory and Experiment II
EditorsM. J. Ablowitz, M. Boiti, F. Pempinelli
PublisherWorld Scientific Publishing
Pages287-294
Number of pages8
ISBN (Electronic)9789814486699
ISBN (Print)9789812382702
DOIs
Publication statusPublished - Apr 2003
EventInternational workshop on nonlinear phenomena 2002 - Gallipoli, Italy
Duration: 27 Jun 20026 Jul 2002

Conference

ConferenceInternational workshop on nonlinear phenomena 2002
CountryItaly
CityGallipoli
Period27/06/026/07/02

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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