Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation

Author:

Alahyane Mohamed1,Chrifi Abderrazak2,Echarroudi Younes3

Affiliation:

1. L2EP, Faculty of Sciences and Technologies , University of Lille , Villeneuve dAscq , France .

2. Department of Mathematics, Faculty of Science and Technology , Cadi Ayyad University , B.P. 549, Av. Abdelkarim Elkhattabi, Guèliz, Marrakesh, 40000 , Morocco .

3. Laboratory of mathematics and population dynamics , Faculty of sciences Semlalia Marrakesh , Morocco .

Abstract

Abstract In this paper, we are interested in some theoretical and numerical studies of a special case of a degenerate nonlinear Schrödinger equation namely the so-called Gross-Pitaevskii Equation(GPE). More precisely, we will treat in a first time the well-posedness of GPE model with a degeneracy occurring in the interior of the space variable domain, i.e ∃x 0 ∈ (0, L), s. t k(x 0) = 0, where k stands for the diffusion coefficient and L is a positive constant. Thereafter, we will focus ourselves on some numerical simulations showing the influence of a different parameters, especially the interior degeneracy, on the behavior of the wave solution corresponding to our model in a special case of the function k namely k(x) = |xx 0| α, α ∈ (0, 1).

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Control and Optimization,Numerical Analysis,Analysis

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