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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.00559 |
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| _version_ | 1866909716287848448 |
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| author | Durán, Angel Reguera, Nuria |
| author_facet | Durán, Angel Reguera, Nuria |
| contents | The present paper is a numerical study of the dynamics of solitary wave solutions of the fractional nonlinear Schrödinger equation, whose existence was analyzed by the authors in the first part of the project. The computational study will be made from the approximation of the periodic initial-value problem with a fully discrete scheme consisting of a Fourier spectral method for the spatial discretization and a fourth-order, Runge-Kutta-Composition method as time integrator. Several issues regarding the stability of the waves, such as the effects of small and large perturbations, interactions of solitary waves and the resolution of initial data into trains of waves are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solitary-wave solutions of the fractional nonlinear Schrödinger equation. II. A numerical study of the dynamics Durán, Angel Reguera, Nuria Numerical Analysis Analysis of PDEs 76B25, 35C07, 65H10 The present paper is a numerical study of the dynamics of solitary wave solutions of the fractional nonlinear Schrödinger equation, whose existence was analyzed by the authors in the first part of the project. The computational study will be made from the approximation of the periodic initial-value problem with a fully discrete scheme consisting of a Fourier spectral method for the spatial discretization and a fourth-order, Runge-Kutta-Composition method as time integrator. Several issues regarding the stability of the waves, such as the effects of small and large perturbations, interactions of solitary waves and the resolution of initial data into trains of waves are discussed. |
| title | Solitary-wave solutions of the fractional nonlinear Schrödinger equation. II. A numerical study of the dynamics |
| topic | Numerical Analysis Analysis of PDEs 76B25, 35C07, 65H10 |
| url | https://arxiv.org/abs/2508.00559 |