Solitons and breathers in sine-Gordon field theory

Using Lamb's diagrammatic technique the most general Backlung transform solution of the sine-Gordon equation was obtained. The collision between a soliton and a breather results in a shift in their positions (spatial shift). Despite this, it is shown that there is no net force between them; periodic solutions exist in which they have zero relative velocity (aggregates). The construction of the sine-Gordon fluctuation vacuum as a coherent state was attempted. The superselection rule between different soliton sectors is discussed.