Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroa oustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.Parametric decays of a circularly polarized wave in an electron–positron plasma, including relativistic effects on the particle motion in the wave field, are studied. The analysis is based on the Vlasov equation in order to account for kinetic effects.Dispersion relations are found for the pump wave and its parametric decays, and they are studied numerically in the weakly relativistic regime. This is done by using a graphical method, which has the advantage of showing explicitly the various modes involved in the decays, making thereby the physical picture more transparent. In a fluid theory three instabilities develop: one is an ordinary decay instability and the other two are modulational instabilities. Some of them involve electroacoustic pseudomodes, which satisfy ?/k?vth.?/k?vth. In the kinetic treatment, although these modes are strongly Landau damped, all three types of instabilities are present. With respect to the fluid results, growth rates either decrease or increase, depending on the nature of the instability. Due to kinetic effects, instability ranges increase relative to the fluid case.FONDECYT318FONDECYT