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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/2505.17026 |
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| _version_ | 1866915300013768704 |
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| author | Holm, Darryl D. Hu, Ruiao Street, Oliver D. Wang, Hanchun |
| author_facet | Holm, Darryl D. Hu, Ruiao Street, Oliver D. Wang, Hanchun |
| contents | We consider a coupled PDE system between the Burgers equation and the KdV equation to model the interactions between `bore'-like structures and wave-like solitons in shallow water. Two derivations of the resulting Burgers-swept KdV system are presented, based on Lie group symmetry and reduced variational principles. Exact compound soliton solutions are obtained, and numerical simulations show that the Burgers and KdV momenta tend toward a balance at which the coupled system reduces to the integrable Gardner equation. The numerical simulations also reveal rich nonlinear solution behaviours that include refraction, reflection, and soliton fusion, before the balance is finally achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion Holm, Darryl D. Hu, Ruiao Street, Oliver D. Wang, Hanchun Pattern Formation and Solitons Mathematical Physics Exactly Solvable and Integrable Systems 35Q35 (Primary), 35Q53, 37K40, 76-10 (Secondary) I.6.3; I.6.5 We consider a coupled PDE system between the Burgers equation and the KdV equation to model the interactions between `bore'-like structures and wave-like solitons in shallow water. Two derivations of the resulting Burgers-swept KdV system are presented, based on Lie group symmetry and reduced variational principles. Exact compound soliton solutions are obtained, and numerical simulations show that the Burgers and KdV momenta tend toward a balance at which the coupled system reduces to the integrable Gardner equation. The numerical simulations also reveal rich nonlinear solution behaviours that include refraction, reflection, and soliton fusion, before the balance is finally achieved. |
| title | Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion |
| topic | Pattern Formation and Solitons Mathematical Physics Exactly Solvable and Integrable Systems 35Q35 (Primary), 35Q53, 37K40, 76-10 (Secondary) I.6.3; I.6.5 |
| url | https://arxiv.org/abs/2505.17026 |