Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form
In the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coeffic...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/7087295 |
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| author | Imre F. Barna Mihály A. Pocsai L. Mátyás |
| author_facet | Imre F. Barna Mihály A. Pocsai L. Mátyás |
| author_sort | Imre F. Barna |
| collection | DOAJ |
| description | In the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case. |
| format | Article |
| id | doaj-art-9c0edf7af051405195b33136dcef5952 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9c0edf7af051405195b33136dcef59522025-02-03T06:45:57ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/70872957087295Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung FormImre F. Barna0Mihály A. Pocsai1L. Mátyás2Wigner Research Center for Physics of the Hungarian Academy of Sciences, Konkoly-Thege Miklós út 29-33, 1121 Budapest, HungaryWigner Research Center for Physics of the Hungarian Academy of Sciences, Konkoly-Thege Miklós út 29-33, 1121 Budapest, HungarySapientia University, Department of Bioengineering, Libertătii Sq. 1, 530104 Miercurea Ciuc, RomaniaIn the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case.http://dx.doi.org/10.1155/2018/7087295 |
| spellingShingle | Imre F. Barna Mihály A. Pocsai L. Mátyás Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form Advances in Mathematical Physics |
| title | Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form |
| title_full | Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form |
| title_fullStr | Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form |
| title_full_unstemmed | Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form |
| title_short | Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form |
| title_sort | self similarity analysis of the nonlinear schrodinger equation in the madelung form |
| url | http://dx.doi.org/10.1155/2018/7087295 |
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