Nonlinear low-frequency electrostatic waves in a magnetised, three-component plasma consisting of warm electrons,warm positrons and cool ions have been investigated. The electrons, positrons and ions are governed by the fluid equations. The system is closed with the Poisson equation. This set of equations is numerically solved for the electric field. The effects of the driving electric field, ion temperature, densities, Mach number, propagation angle and drift velocity of different species are investigated. It is shown that depending on the driving electric field, temperature, densities, Mach number, propagation angle and drift velocity of different species on the nonlinear wave structures components, the numerical solutions exhibit waveforms that are sinusoidal, saw-tooth and spiky. The results are compared with satellite observations.