A Theoretical Framework for Modelling Non-Linear Wave Propagation in Nigerian Ionospheric Plasma

Non-linear wave propagation in ionospheric plasma, including the generation and evolution of equatorial plasma bubbles and spread-F structures, represents a fundamental scientific challenge with direct implications for the reliability of satellite navigation and HF radio communication over Nigeria's equatorial region. This study develops a theoretical framework and computational model for non-linear wave propagation in Nigerian ionospheric plasma, extending established fluid plasma models to incorporate the distinctive characteristics of the African equatorial electrojet and thermospheric wind patterns. A generalised non-linear Schrodinger equation adapted for anisotropic magnetised plasma is derived and solved numerically using a split-step Fourier method. The model incorporates realistic ionospheric background profiles derived from the IRI-2020 model parameterised for the West African sector using data from the Nigerian GNSS Reference Network and ionosonde measurements from the University of Ibadan. Plasma bubble generation mechanisms including E-B instability and gravitational Rayleigh-Taylor instability are implemented. Simulation outputs are validated against observed S4 scintillation and TEC depletion events from CORS station data. The framework reveals that the pre-reversal enhancement of the F-region electric field in the West African longitude sector has distinctive non-linear plasma wave consequences that produce more structured and extended bubble morphologies than predicted by linear instability theory. Keywords: non-linear wave propagation, ionospheric plasma, equatorial plasma bubble, Nigeria, Schrodinger equation