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On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions

Abstract : We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schrödinger type and have recently been obtained by Dumas et al. in the context of nonlinear optics. In contrast to the usual nonlinear Schrödinger equation, this new model incorporates the additional effects of self-steepening and partial off-axis variations of the group velocity of the laser pulse. We prove global-in-time existence of the corresponding solution for various choices of parameters. In addition, we present a series of careful numerical simulations concerning the (in-)stability of stationary states and the possibility of finite-time blow-up.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02303267
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mercredi 2 octobre 2019 - 10:42:44
Dernière modification le : jeudi 3 octobre 2019 - 01:09:43

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Jack Arbunich, Christian Klein, Christof Sparber. On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2019, 53 (5), pp.1477-1505. ⟨10.1051/m2an/2019018⟩. ⟨hal-02303267⟩

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