[en] Nonlinear interaction of electromagnetic waves and acoustic modes in an electron-positron plasma is investigated. The plasma of electrons and positrons is quite plastic so that the imposition of electromagnetic (EM) waves causes depression of the plasma and other structural imprints on it through either the nonresonant or resonant interaction. Our theory shows that the nonresonant interaction can lead to the coalescence of photons and collapse of plasma cavity in higher (≥ 2) dimensions. The resonant interaction, in which the group velocity of EM waves is equal to the phase velocity of acoustic waves, is analyzed and a set of basic equations of the system is derived via the reductive perturbation theory. We find new solutions of solitary types: bright solitons, kink solitons, and dark solitons as the solutions to these equations. Our computation hints their stability. An impact of the present theory on astrophysical plasma settings is expected, including the cosmological relativistically hot electron-positron plasma. 20 refs., 9 figs