We extend the asymptotic factorisation theorem for the canonical field--theoretic symplectic form from a single kink--antikink pair to an arbitrary number N of well--separated kinks in a general relativistic scalar field theory with degenerate vacua. The configuration is modelled by a superposition of N single--kink Cauchy data with independent centres and velocities. We prove that the pullback of the canonical symplectic form to the 2N--dimensional parameter space factorises into the sum of N free--kink symplectic forms plus off--diagonal corrections that are exponentially small in the minimum separation between any two solitons. The error is bounded by O\! (e^- D_{/2}), where is the decay rate of the static kink and D_ the minimal separation. The result is universal and does not rely on integrability or closed--form solutions. The leading--order symplectic structure is a product of free--particle phase spaces, providing a rigorous geometric foundation for the quantum mechanics of asymptotically free multi--kink states in non--integrable models.
Timmermans et al. (Wed,) studied this question.