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Journal Articles Zeitschrift für Angewandte Mathematik und Physik Year : 2013

Justification of a nonlinear Schrödinger model for laser beams in photopolymers

Abstract

A nonstationary model that relies on the spatial nonlinear Schrödinger (NLS) equation with the time-dependent refractive index describes laser beams in photopolymers. We consider a toy problem, when the rate of change of refractive index is proportional to the squared amplitude of the electric field and the spatial domain is a plane. After formal derivation of the NLS approximation from a two-dimensional quasilinear wave equation, we establish local well-posedness of the original and reduced models and perform rigorous justification analysis to control smallness of the approximation error for appropriately small times.
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Dates and versions

hal-00917025 , version 1 (11-12-2013)

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Dmitry E. Pelinovsky, Dmitry Ponomarev. Justification of a nonlinear Schrödinger model for laser beams in photopolymers. Zeitschrift für Angewandte Mathematik und Physik, 2013, ⟨10.1007/s00033-013-0338-9⟩. ⟨hal-00917025⟩
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