Numerical study of self-focusing solutions to the Schrödinger-Debye system

Christophe Besse (1) , Brigitte Bidégaray (1)

1 MIP - Mathématiques pour l'Industrie et la Physique

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.

Mots clés: Nonlinear optics; Schrödinger-like equations; relaxation method; split-step method; self-focusing

Domaines: Analyse numérique [math.NA]

Christophe Besse, Brigitte Bidégaray. Numerical study of self-focusing solutions to the Schrödinger-Debye system. ESAIM: Mathematical Modelling and Numerical Analysis, 2001, 35 (1), pp.35-55. ⟨10.1051/m2an:2001106⟩. ⟨hal-00319989⟩