This work investigates the role of coherent structure preservation in nonlinear dynamical systems exhibiting finite-time singularity formation (blowup), focusing on the one-dimensional focusing quintic nonlinear Schrödinger equation. Building on modern advances in nonlinear PDE analysis, particularly the decomposition of solutions into coherent structures such as solitons, we introduce an operational coherence measure that quantifies the projection of a solution onto the soliton manifold over time. Through numerical simulations, we identify three distinct dynamical regimes: stable solitonic propagation, dispersive decay, and supercritical concentration. In the blowup regime, we demonstrate that while the characteristic spatial scale collapses, a non-vanishing fraction of the solution remains localized in L², indicating the persistence of a coherent core. Simultaneously, the amplitude follows the critical scaling law \|u\|_ ^-1/2 with high accuracy, consistent with established theoretical results. These findings support a reinterpretation of blowup as a process of coherent concentration rather than complete structural breakdown. This perspective provides a unifying framework for understanding stability, singularity formation, and structural persistence in nonlinear systems, and establishes a conceptual bridge between nonlinear PDE theory and coherence-based frameworks such as Δ-coherence. The results are supported by reproducible numerical experiments, including a full Python implementation of the split-step Fourier method and soliton projection fitting procedure.
Eduardo Parra (Mon,) studied this question.