  We present for the first time the nonlinear dynamics of quantum
electrodynamic (QED) photon splitting in a strongly magnetized
electron-positron (pair) plasma. By using a QED corrected Maxwell equation, we
derive a set of equations that exhibit nonlinear couplings between
electromagnetic (EM) waves due to nonlinear plasma currents and QED
polarization and magnetization effects. Numerical analyses of our coupled
nonlinear EM wave equations reveal the possibility of a more efficient decay
channel, as well as new features of energy exchange among the three EM modes
that are nonlinearly interacting in magnetized pair plasmas. Possible
applications of our investigation to astrophysical settings, such as magnetars,
are pointed out.
