Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability
The hyperbolic nonlinear Schrödinger equation in the (3 + 1)-dimension depicts the evolution of the elevation of the water wave surface for slowly modulated wave trains in deep water. Many researchers have studied the applicability and practicality of this model, but the analytical approach has been...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9050272 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565661673455616 |
|---|---|
| author | Vikas Kumar Ram Jiwari Aloev Rakhmatullo Djurayevich Mirzoali Urazaliyevich Khudoyberganov |
| author_facet | Vikas Kumar Ram Jiwari Aloev Rakhmatullo Djurayevich Mirzoali Urazaliyevich Khudoyberganov |
| author_sort | Vikas Kumar |
| collection | DOAJ |
| description | The hyperbolic nonlinear Schrödinger equation in the (3 + 1)-dimension depicts the evolution of the elevation of the water wave surface for slowly modulated wave trains in deep water. Many researchers have studied the applicability and practicality of this model, but the analytical approach has been virtually absent from the literature. We adapted the lie symmetry analysis method to obtain a new complex solution in this work. The obtained complex solution contains bright and dark solitons. Furthermore, modulation instability is applied to this model to explain the interplay between nonlinear and dispersive effects. As a result, the modulation instability condition and the explosive rate are also discussed. |
| format | Article |
| id | doaj-art-98d113ccc6c84237aa73cb01646207d3 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-98d113ccc6c84237aa73cb01646207d32025-02-03T01:06:57ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9050272Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation InstabilityVikas Kumar0Ram Jiwari1Aloev Rakhmatullo Djurayevich2Mirzoali Urazaliyevich Khudoyberganov3Department of MathematicsDepartment of MathematicsDepartment of Computational Mathematics and Information SystemsDepartment of Computational Mathematics and Information SystemsThe hyperbolic nonlinear Schrödinger equation in the (3 + 1)-dimension depicts the evolution of the elevation of the water wave surface for slowly modulated wave trains in deep water. Many researchers have studied the applicability and practicality of this model, but the analytical approach has been virtually absent from the literature. We adapted the lie symmetry analysis method to obtain a new complex solution in this work. The obtained complex solution contains bright and dark solitons. Furthermore, modulation instability is applied to this model to explain the interplay between nonlinear and dispersive effects. As a result, the modulation instability condition and the explosive rate are also discussed.http://dx.doi.org/10.1155/2022/9050272 |
| spellingShingle | Vikas Kumar Ram Jiwari Aloev Rakhmatullo Djurayevich Mirzoali Urazaliyevich Khudoyberganov Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability Journal of Mathematics |
| title | Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability |
| title_full | Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability |
| title_fullStr | Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability |
| title_full_unstemmed | Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability |
| title_short | Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability |
| title_sort | hyperbolic 3 1 dimensional nonlinear schrodinger equation lie symmetry analysis and modulation instability |
| url | http://dx.doi.org/10.1155/2022/9050272 |
| work_keys_str_mv | AT vikaskumar hyperbolic31dimensionalnonlinearschrodingerequationliesymmetryanalysisandmodulationinstability AT ramjiwari hyperbolic31dimensionalnonlinearschrodingerequationliesymmetryanalysisandmodulationinstability AT aloevrakhmatullodjurayevich hyperbolic31dimensionalnonlinearschrodingerequationliesymmetryanalysisandmodulationinstability AT mirzoaliurazaliyevichkhudoyberganov hyperbolic31dimensionalnonlinearschrodingerequationliesymmetryanalysisandmodulationinstability |