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self-focusing.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Numerical study of self-focusing solutions to the Schrödinger-Debye system
Christophe Besse, Brigitte Bidégaray
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 35 / Issue 1 / January 2001

Published online by Cambridge University Press:

15 April 2002, pp. 35-55

Print publication:

January 2001
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In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.