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This paper presents a theoretical and numerical study of all possible nonlinear electrostatic waves in an unmagnetized and collisionless electron–positron plasma. From a two-component plasma with an arbitrary ion/positron-to-electron mass ratio β and a temperature ratio TR, four possible waves are discussed: Langmuir waves (LWs), electron acoustic waves, ion acoustic waves, and ion-bulk (IBk) waves. Although LWs are ubiquitous, the existence of the other three acoustic waves depends on the values of β and TR. In an electron–positron plasma, only LWs and IBk waves are allowed. The dispersion relation of these waves varies from a “thumb” curve to a “thumb–teardrop” curve when TR < 1. Vlasov simulations are used to verify predicted waves and reveal several characteristics of excited waves, such as sideband instability, harmonic effect, and nonlinear shifts in frequency and wave number. The present results for an electron–positron plasma can be easily applied to plasmas with arbitrary β and TR, especially when the dispersion relations of these waves are close to each other.

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