Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model
Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations. We will show that solitary wave solutions are recovered throug...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2022-05-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2022-0018 |
| _version_ | 1811329539267100672 |
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| author | Bica Ion Mucalica Ana |
| author_facet | Bica Ion Mucalica Ana |
| author_sort | Bica Ion |
| collection | DOAJ |
| description | Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations. We will show that solitary wave solutions are recovered through a limiting process after the elliptic modulus of the Jacobi elliptic function cn that describes the periodic solutions for the self-focusing nonlinear Schrödinger model. |
| first_indexed | 2024-04-13T15:45:40Z |
| format | Article |
| id | doaj.art-ae4e7406952346b2b9d47200ee6e18d3 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-13T15:45:40Z |
| publishDate | 2022-05-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-ae4e7406952346b2b9d47200ee6e18d32022-12-22T02:41:00ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352022-05-01302456210.2478/auom-2022-0018Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger ModelBica Ion0Mucalica Ana1Department of Mathematics and Statistics, MacEwan University, 10700 104 Ave NW, Edmonton, AB, Canada, T5J 4S2.Department of Mathematics and Statistics, MacEwan University, 10700 104 Ave NW, Edmonton, AB, Canada, T5J 4S2.Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations. We will show that solitary wave solutions are recovered through a limiting process after the elliptic modulus of the Jacobi elliptic function cn that describes the periodic solutions for the self-focusing nonlinear Schrödinger model.https://doi.org/10.2478/auom-2022-0018nlsself-focusingdefocusingdispersivenonlinearitycarrier wavessolution profileenvelopecnoidal wavessolitary wavessurface gravity wavessound waveswater-air interfacesonic layer depthprimary 33e05, 35q55secondary 35q53 |
| spellingShingle | Bica Ion Mucalica Ana Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica nls self-focusing defocusing dispersive nonlinearity carrier waves solution profile envelope cnoidal waves solitary waves surface gravity waves sound waves water-air interface sonic layer depth primary 33e05, 35q55 secondary 35q53 |
| title | Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model |
| title_full | Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model |
| title_fullStr | Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model |
| title_full_unstemmed | Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model |
| title_short | Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model |
| title_sort | periodic and solitary wave solutions for the one dimensional cubic nonlinear schrodinger model |
| topic | nls self-focusing defocusing dispersive nonlinearity carrier waves solution profile envelope cnoidal waves solitary waves surface gravity waves sound waves water-air interface sonic layer depth primary 33e05, 35q55 secondary 35q53 |
| url | https://doi.org/10.2478/auom-2022-0018 |
| work_keys_str_mv | AT bicaion periodicandsolitarywavesolutionsfortheonedimensionalcubicnonlinearschrodingermodel AT mucalicaana periodicandsolitarywavesolutionsfortheonedimensionalcubicnonlinearschrodingermodel |