Focusing at a Point with Caustic Crossing for a Class of Nonlinear Equations
نویسندگان
چکیده
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 Schrödinger equations. We apply them to Hartree, Klein-Gordon and wave equations.
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