Where solitons are in a KdV soliton gas (opens in new tab)

The Korteweg-De Vries (KdV) equation is a paradigmatic model of integrable classical fields, admitting solitoning solutions. When many solitons are near to each other, their shapes are modified, and it is not manifest, from the KdV field, where they are. This is a key problem in the analysis of a soliton gas, as its main object, the density of states, is a number of solitons per unit length. How to define solitons' positions at finite densitie...