  Given a solution of a nonlinear wave equation on the flat space-time (with a
real analytic nonlinearity), we relate its Cauchy data at two different times
by nonlinear representation formulas in terms of asymptotic series. We first
show how to construct formally these series by mean of generating functions
based on an algebraic framework inspired by the construction of Fock spaces in
quantum field theory. Then we build an analytic setting in which all these
constructions really make sense and give rise to convergent series.
