Recently, heat conduction in low-dimensional materials has attracted much attention. The energy carriers responsible for the heat conduction in the Fermi-Pasta-Ulam (FPU) β lattice is still in debate. To the best of our knowledge, the sound velocity of energy transfer has been measured to examine the properties of the energy carriers, by using both nonequilibrium and equilibrium approaches. Nevertheless, the uncertainty of the computational data is too large to distinguish between the two predictions based on soliton theory and effective-phonon theory. In this paper, the spatiotemporal propagation of a momentum excitation traveling along the FPU-β lattice is investigated. The harmonic and anharmonic couplings induce the dispersion and localization of a energy packet on the lattice, respectively. The bifurcation of a solitary wave takes place as the energy of the packet exceeds a threshold. Based on the "acoustic vacuum" phenomenon in the pure quartic lattice, a two-segment lattice composed of the FPU-β chain and the pure quartic chain is constructed. The heat flux in the two-segment lattice is studied to compare with that in the FPU-β lattice. The ratio of the heat flux of the two-segment lattice to the FPU-β lattice increases monotonically as temperature rises. We conclude that phonons are the majority energy carriers in the low temperature regime, while solitons become dominant carriers as the temperature increases. The spatiotemporal propagation of a momentum excitation traveling along the two-segment lattice is also investigated. Phonon packets excited in the FPU-β part are reflected at the interface while solitary waves can pass through the interface. This supports microscopically our conclusion on the energy carriers in the FPU-β lattice.