Conserved quantities and generalized solutions of the ultradiscrete KdV equation

Abstract

We construct generalized solutions to the ultradiscrete KdV equation, including the so-called negative solition solutions. The method is based on the ultradiscretization of soliton solutions to the discrete KdV equation with gauge transformation. The conserved quantities of the ultradiscrete KdV equation are shown to be constructed in a similar way to those for the box-ball system.

16 pages, 7 figures

References in corpus (2)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Fundamental Cycle of a Periodic Box-Ball System

Cited by in corpus (5)

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• Bi-infinite solutions for KdV- and Toda-type discrete integrable systems based on path encodings
• From Polygons to Ultradiscrete Painlevé Equations
• The generalized periodic ultradiscrete KdV equation and its background solutions
• Darboux dressing and undressing for the ultradiscrete KdV equation