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A set of nonlinear equations which can self-consistently describe the behavior of high frequency Electromagnetic (EM) waves in un-magnetized, ultra-relativistic electron-positron (e-p) plasmas is obtained on the basis of Vlasov-Maxwell equations. Nonlinear wave-wave, wave-particle interactions lead to the coupling of high frequency EM waves with low frequency density perturbations which result from EM waves radiation pressure. The same as that in conventional electron-ion (e-i) plasmas, strong EM waves in e-p plasmas will give rise to density depletion in which itself are trapped. But on the contrary to that in e-i plasmas, there no longer exists electrostatic acoustic-like wave in e-p plasmas due to the absence of mass difference. For linear polarized EM waves, a stationary EM soliton with a spiky structure will be formed. The possible relation of the localized field to pulsar radio pulse is discussed.