Amplitude analysis of $D^{+} rightarrow K_{S}^{0} pi^{+} pi^{+} pi^{-}$

The decay $D^{+} rightarrow K_{S}^{0} pi^{+} pi^{+} pi^{-}$ is studied with an amplitude analysis using a data set of 2.93${mbox{,fb}^{-1}}$ of $e^+e^+$ collisions at the $psi(3770)$ peak accumulated by the BESIII detector. Intermediate states and non-resonant 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 quasi-two-body decays $ K_{S}^{0} a_{1}(1260)^{+}$, $ bar{K}_{1}(1270)^{0} pi^{+}$ $ bar{K}_{1}(1400)^{0} pi^{+}$, $ bar{K}_{1}(1650)^{0} pi^{+}$, and $ bar{K}(1460)^{0} pi^{+}$, a three-body decays $K_{S}^{0}pi^{+}rho^{0}$, as well as a non-resonant component $ K_{S}^{0}pi^{+}pi^{+}pi^{-}$. The dominant amplitude is $ K_{S}^{0} a_{1}(1260)^{+}$, with a fit fraction of $(40.3pm2.1pm2.9)%$, where the first and second uncertainties are statistical and systematic, respectively.