### Abstract

Various evolution equations from mathematical physics conserve one or more integrals (constants of the motion; e.g. the energy) and have solutions in the form of steadily propagating waves (e.g. solitairy waves). In spatial discretizations these properties are generally lost. However, observing that the properties are a consequence of a certain variational structure (Poisson structL!re) of the evolution equation, we derive discretizations in such a way that they inherit this structure. Consequently the constants of the motion and the existence of steadily propagating

waves are conserved.

Calculations are shown for the Korteweg-de Vries equation as an example.

waves are conserved.

Calculations are shown for the Korteweg-de Vries equation as an example.

Original language | English |
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Pages | 17-35 |

Publication status | Published - 1987 |

Event | 1st International Conference on Industrial and Applied Mathematics, ICIAM 1987 - Paris-La Vilette, France Duration: 20 Jun 1987 → 3 Jul 1987 Conference number: 1 |

### Conference

Conference | 1st International Conference on Industrial and Applied Mathematics, ICIAM 1987 |
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Abbreviated title | ICIAM 1987 |

Country | France |

City | Paris-La Vilette |

Period | 20/06/87 → 3/07/87 |

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## Cite this

van Beckum, F. P. H., & van Groesen, E. (1987).

*Discretizations conserving energy and other constants of the motion*. 17-35. Paper presented at 1st International Conference on Industrial and Applied Mathematics, ICIAM 1987, Paris-La Vilette, France.