Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation
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 i...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2022-05-01
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| Series: | Moroccan Journal of Pure and Applied Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/mjpaa-2022-0018 |
| _version_ | 1828337488461037568 |
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| author | Alahyane Mohamed Chrifi Abderrazak Echarroudi Younes |
| author_facet | Alahyane Mohamed Chrifi Abderrazak Echarroudi Younes |
| author_sort | Alahyane Mohamed |
| collection | DOAJ |
| description | 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). |
| first_indexed | 2024-04-13T22:15:55Z |
| format | Article |
| id | doaj.art-d0b0a114e45948a19abad8d6781f12f3 |
| institution | Directory Open Access Journal |
| issn | 2351-8227 |
| language | English |
| last_indexed | 2024-04-13T22:15:55Z |
| publishDate | 2022-05-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Moroccan Journal of Pure and Applied Analysis |
| spelling | doaj.art-d0b0a114e45948a19abad8d6781f12f32022-12-22T02:27:32ZengSciendoMoroccan Journal of Pure and Applied Analysis2351-82272022-05-018225627810.2478/mjpaa-2022-0018Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equationAlahyane Mohamed0Chrifi Abderrazak1Echarroudi Younes2L2EP, Faculty of Sciences and Technologies, University of Lille, 59655Villeneuve dAscq, France.Department of Mathematics, Faculty of Science and Technology, Cadi Ayyad University, B.P. 549, Av. Abdelkarim Elkhattabi, Guèliz, Marrakesh, 40000, Morocco.Laboratory of mathematics and population dynamics, Faculty of sciences Semlalia Marrakesh, Morocco.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).https://doi.org/10.2478/mjpaa-2022-0018cubic schrödinger equationtime-dependent schrödinger equationinterior degeneracycranknicolson methodgalerkin method35k6535q4035q4135j1065p40 |
| spellingShingle | Alahyane Mohamed Chrifi Abderrazak Echarroudi Younes Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation Moroccan Journal of Pure and Applied Analysis cubic schrödinger equation time-dependent schrödinger equation interior degeneracy cranknicolson method galerkin method 35k65 35q40 35q41 35j10 65p40 |
| title | Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation |
| title_full | Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation |
| title_fullStr | Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation |
| title_full_unstemmed | Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation |
| title_short | Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation |
| title_sort | theoretical and numerical analysis of a degenerate nonlinear cubic schrodinger equation |
| topic | cubic schrödinger equation time-dependent schrödinger equation interior degeneracy cranknicolson method galerkin method 35k65 35q40 35q41 35j10 65p40 |
| url | https://doi.org/10.2478/mjpaa-2022-0018 |
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