A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV Systems

• URL: http://arxiv.org/abs/2604.10474v1
• Date: Sun, 12 Apr 2026 06:04:30 GMT
• Title: A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV Systems
• Abstract summary: We investigate the integrable structure and soliton dynamics of a coupled modified Korteweg-de Vries (cmKdV) system with a real symmetric coupling matrix.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 multicomponent 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.

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