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

First integrals for non linear hyperbolic equations