  It was conjectured that the classical bosonic string in AdS times a sphere
has a special action variable which corresponds to the length of the operator
on the field theory side. We discuss the analogous action variable in the
sine-Gordon model. We explain the relation between this action variable and the
Backlund transformations and show that the corresponding hidden symmetry acts
on breathers by shifting their phase. It can be considered a nonlinear analogue
of splitting the solution of the free field equations into the positive- and
negative-frequency part.
