Using a combination of time-dependent density matrix renormalization group and single mode approximation, we investigate the dynamical structure factor of spin chains with antiferromagnetic nearest-neighbor J₁, next-nearest-neighbor J₂, and three-site J₃ interactions and show that, in all gapped phases and at the transitions between them, a simple physical picture can be obtained in terms of magnons and spin-1/2 domain-wall excitations or spinons. This applies to the fully dimerized phase, where a magnon mode clearly pops out of the two-spinon continuum for spin-1 and spin-3/2, and to the transition between the dimerized phase and the Haldane phase (resp. partially dimerized phase) for spin-1 (resp. spin-3/2), where spinons are deconfined along the transition but get confined across it when it is first order. Implications for the interpretation of inelastic neutron scattering in spin chains are briefly discussed.

We study the dynamical structure factor of the frustrated spin-3/2 J₁-J₂ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid Ansatz corroborated by density-matrix renormalization-group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at J₂ ≈ 0.32J₁, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at J₂ ≈ 0.4J₁ beyond the Lifshitz point (J₂ ≈ 0.388J₁). The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin-5/2 case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.