Focusing at a point with caustic crossing for a class of nonlinear equations

Details Focusing at a point with caustic crossing for a class of nonlinear equations Focusing at a point with caustic crossing for a class of nonlinear equations

2003-01-14

arxiv.org/abs/math/0301144v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

We consider the asymptotic behavior of solutions to nonlinear partial differential equations in the limit of short wavelength. For initial data which cause focusing at one point, we highlight critical indexes as far as the influence of the nonlinearity in the neighborhood of the caustic is concerned. Our results generalize some previous ones proved by the first author in the case of nonlinear Schrodinger equations. We apply them to Hartree, Klein-Gordon and wave equations.

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