Solitons in the Korteweg-de Vries Equation
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918157644464128 |
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| author | Bueno, G. Bonehill, M. |
| author_facet | Bueno, G. Bonehill, M. |
| contents | We propose a numerical solution to the Korteweg-de Vries (KdV) equation using a Crank-Nicolson scheme, and compare its performance to the Fast Fourier Transform method. The properties and interactions of soliton solutions are further examined. Initial conditions were varied to analyse soliton formation in the resulting system. Performing an L$^2$ error analysis demonstrated consistency between numerical methods of solving the KdV equation and analytical solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solitons in the Korteweg-de Vries Equation Bueno, G. Bonehill, M. Pattern Formation and Solitons Exactly Solvable and Integrable Systems We propose a numerical solution to the Korteweg-de Vries (KdV) equation using a Crank-Nicolson scheme, and compare its performance to the Fast Fourier Transform method. The properties and interactions of soliton solutions are further examined. Initial conditions were varied to analyse soliton formation in the resulting system. Performing an L$^2$ error analysis demonstrated consistency between numerical methods of solving the KdV equation and analytical solutions. |
| title | Solitons in the Korteweg-de Vries Equation |
| topic | Pattern Formation and Solitons Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2510.07207 |