Abstract
By means of numerical experiments, the Zabusky-Kruskal discretization of the Korteweg-de Vries equation, is shown to have solitary saw-toothed wave packet solutions. An analysis is presented to explain the properties of this type of solution. This, as well as numerical experiments indicate that the solution is stable only for small amplitude wave packets and that the propagation of the wave packet is essentially linear. Similar experiments and analysis for a discretized modified-Korteweg-de Vries equation show that large amplitude solitary wave packet solutions are possible for this equation and that their propagation is governed by an MKdV equation which differs from the one which is consistent with the discretized equation. This makes it possible to construct sawtoothed wave packets which behave like MKdV-solitons. The results of several numerical experiments showing collisions between wave packets and solitons are also reported.
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