Amplitude analysis of ${D}^{+}\to {K}_{S}^{0}{\pi }^{+}{\pi }^{+}{\pi }^{-}$

The decay ${D}^{+}\to {K}_{S}^{0}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ is studied with an amplitude analysis using a data set of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}$ collisions at the $\psi \left(3770\right)$ peak accumulated by the BESIII detector. Intermediate states and nonresonant components, and their relative fractions and phases, have been determined. The significant amplitudes, which contribute to the model that best fits the data, are composed of five quasitwo-body decays ${K}_{S}^{0}{a}_{1}\left(1260{\right)}^{+}$, ${\overline{K}}_{1}\left(1270{\right)}^{0}{\pi }^{+}$ ${\overline{K}}_{1}\left(1400{\right)}^{0}{\pi }^{+}$, ${\overline{K}}_{1}\left(1650{\right)}^{0}{\pi }^{+}$, and $\overline{K}\left(1460{\right)}^{0}{\pi }^{+}$, a three-body decay ${K}_{S}^{0}{\pi }^{+}{\rho }^{0}$, as well as a nonresonant component ${K}_{S}^{0}{\pi }^{+}{\pi }^{+}{\pi }^{-}$. The dominant amplitude is ${K}_{S}^{0}{a}_{1}\left(1260{\right)}^{+}$, with a fit fraction of $\left(40.3±2.1±2.9\right)%$, where the first and second uncertainties are statistical and systematic, respectively.