### Abstract

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 |

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### Cite this

*Discretizations conserving energy and other constants of the motion*. 17-35.

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**Discretizations conserving energy and other constants of the motion.** / van Beckum, F.P.H.; van Groesen, E.

Research output: Contribution to conference › Paper

TY - CONF

T1 - Discretizations conserving energy and other constants of the motion

AU - van Beckum, F.P.H.

AU - van Groesen, E.

PY - 1987

Y1 - 1987

N2 - 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 propagatingwaves are conserved.Calculations are shown for the Korteweg-de Vries equation as an example.

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

M3 - Paper

SP - 17

EP - 35

ER -