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Original Articles

On Negatons of the Toda Lattice

Pages 181-193 | Published online: 21 Jan 2013
 

Abstract

Negatons are a solution class with the following characteristic properties: They consist of solitons which are organized in groups. Solitons belonging to the same group are coupled in the sense that they drift apart from each other only logarithmically. The groups themselves rather behave like particles. Moving with constant velocity, they collide elastically with the only effect of a phase-shift. The main result of this article is the rigorous proof of this characterization (including an explicit formula for the phase-shift) in terms of the asymptotic behaviour. To illustrate our result, we also discuss prototypical examples.

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