A visual approach to the ultradiscrete KdV equation with non-integer site values

Abstract

Simple visual approaches are used to examine the ultradiscrete KdV equation with arbitrary real values for the dependent variable. The number and sizes of the solitons in the system can be obtained straightforwardly using these visualizations. By identifying the initial soliton sizes and positions, the initial profile can be decomposed into its constituent parts, which can then be evolved separately, and then the evolved profile can be reconstructed.