1. Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation
- Author
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Alahyane Mohamed, Chrifi Abderrazak, and Echarroudi Younes
- Subjects
cubic schrödinger equation ,time-dependent schrödinger equation ,interior degeneracy ,cranknicolson method ,galerkin method ,35k65 ,35q40 ,35q41 ,35j10 ,65p40 ,Mathematics ,QA1-939 - 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 ∃x0 ∈ (0, L), s. t k(x0) = 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) = |x − x0| α, α ∈ (0, 1).
- Published
- 2022
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