Mathematics – Analysis of PDEs
Scientific paper
2007-04-20
Mathematics
Analysis of PDEs
38 pages, 1 figure, v2: some sign conventions have been changed, some minor corrections has been added
Scientific paper
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.
Harrivel Dikanaina
Hélein Frédéric
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