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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2604.10474 |
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| _version_ | 1866911674965950464 |
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| author | Delisle, Laurent Jaouadi, Amine |
| author_facet | Delisle, Laurent Jaouadi, Amine |
| contents | We investigate the integrable structure and soliton dynamics of a coupled modified Korteweg-de Vries (cmKdV) system with a real symmetric coupling matrix. We introduce a vector reformulation of Hirota's bilinear formalism in which both the bilinear equations and their solutions are expressed directly at the vector level, rather than through a component-wise construction. This formulation preserves the intrinsic structure of the coupled system and provides a compact framework for multi-component nonlinear wave dynamics. Within this approach, we construct explicit one-, two-, and three-soliton solutions in closed vector form and recover the three-soliton condition directly at the vector level, confirming consistency with integrability. The method enables a unified treatment of focusing, defocusing, and mixed-sign regimes. In particular, for indefinite coupling, it reveals the existence of nontrivial vector ground states, leading to soliton solutions on non-zero backgrounds. These results highlight the structural advantages of the vector bilinear approach and open perspectives for the study of more general nonlinear excitations in multi-component integrable systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10474 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV Systems Delisle, Laurent Jaouadi, Amine Exactly Solvable and Integrable Systems Quantum Physics We investigate the integrable structure and soliton dynamics of a coupled modified Korteweg-de Vries (cmKdV) system with a real symmetric coupling matrix. We introduce a vector reformulation of Hirota's bilinear formalism in which both the bilinear equations and their solutions are expressed directly at the vector level, rather than through a component-wise construction. This formulation preserves the intrinsic structure of the coupled system and provides a compact framework for multi-component nonlinear wave dynamics. Within this approach, we construct explicit one-, two-, and three-soliton solutions in closed vector form and recover the three-soliton condition directly at the vector level, confirming consistency with integrability. The method enables a unified treatment of focusing, defocusing, and mixed-sign regimes. In particular, for indefinite coupling, it reveals the existence of nontrivial vector ground states, leading to soliton solutions on non-zero backgrounds. These results highlight the structural advantages of the vector bilinear approach and open perspectives for the study of more general nonlinear excitations in multi-component integrable systems. |
| title | A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV Systems |
| topic | Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2604.10474 |