Abstract
New solutions to the ultradiscrete soliton equations, such as the Box–Ball system, the Toda equation, etc. are obtained. One of the new solutions which we call a “negative‐soliton” satisfies the ultradiscrete KdV equation (Box–Ball system) but there is not a corresponding traveling wave solution for the discrete KdV equation. The other one which we call a “static‐soliton” satisfies the ultradiscrete Toda equation but there is not a corresponding traveling wave solution for the discrete Toda equation. A collision of a soliton with a negative‐soliton generates many balls in a box over the capacity of the box in the Box–Ball system, while a collision of a soliton with the static‐soliton describes, in the ultradiscrete limit, transmission of a soliton through junctions of a “nonuniform Toda equation.” We have obtained exact solutions describing these phenomena.
Published Version
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