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D.E. Pelinovsky and D.V. Ponomarev

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Justification of a nonlinear Schrödinger model for laser beams in photopolymers

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Z. Angew. Math. Phys. 65 (2014), 405-433

**Abstract:**

A nonstationary model that relies on the nonlinear Schrodinger (NLS)
equation with the timedependent
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 R^{2}. After formal derivation of the NLS approximation from a
two-dimensional quasi-linear wave equation, we establish local well-posedness of the original and reduced
models and perform rigorous justification analysis to establish smallness of the approximation
error for appropriately small time intervals. Numerical simulations are developed to illustrate the
approximation result in the one-dimensional case.

**Keywords:**

Nonlinear optics, nonlinear Schrodinger equation, justification of amplitude equations, energy estimates,
local well-posedness.