Dualism in the Theory of Soliton Solutions

The dualism of the theories of soliton solutions and solutions to functional differential equations of pointwise type is discussed. We describe the foundations underlying the formalism of this dualism, the central element of which is the concept of a soliton bouquet, as well as a dual pair “function–operator.” Within the framework of this approach, it is possible to describe the entire space of soliton solutions with a given characteristic and their asymptotics in both space and time. As an example, the model of traffic flow on the Manhattan lattice is used to describe the whole family of bounded soliton solutions.