Pulsar magnetospheres are composed of electron-positron plasmas characterised by broadband electromagnetic emission, the source of which remains elusive. This paper investigates one possible emission mechanism in which electrostatic oscillations are coupled to propagating electromagnetic waves by the magnetic field inhomogeneity, thus creating a source of radiation in the pulsar magnetosphere. The full nonlinear equations in cylindrical geometry for a streaming cold electron-positron plasma are solved numerically, together with Maxwell's equations, using a Finite-Difference Time Domain method. Electrostatic oscillations are induced in a streaming plasma in the presence of a non-uniform magnetic field, and the resulting electromagnetic waves are modelled self-consistently. Also presented is the linear perturbation analysis of these model equations perturbed from a dynamical equilibrium in order to probe the fundamental modes present in the system. These simulations successfully exhibit the coupling mechanism and the nonlinear interaction between electromagnetic waves and independent plasma oscillations, confirming the importance of coherent plasma effects and collective plasma processes in the pulsar magnetosphere.