The rising menace of unknown gunmen in the South-East region of Nigeria poses significant socio-political and security challenges. Traditional approaches to analyzing such insurgent dynamics often fail to capture the sudden, sporadic, and highly nonlinear nature of violent outbreaks. In this study, we apply the rogue wave equation, derived from the nonlinear Schrödinger (NLS) framework, as a mathematical tool to model the emergence and amplification of violent incidents associated with unknown gunmen. The rogue wave equation is coupled with a set of socio-environmental ordinary differential equations (ODEs) representing community grievances, misinformation, policing strength, and economic stress. Stability analysis reveals thresholds where small disturbances can escalate into large-scale violent events, analogous to the modulation instability that produces rogue waves in physical systems. Numerical simulations, carried out using the Split-Step Fourier Method (for the NLS component) and Runge–Kutta scheme (for the ODEs), generate wave-like patterns that illustrate the intermittent surges of violence. Results show that bursts of violent activity are most likely when community grievances and misinformation exceed critical levels, while strong policing and economic stability serve as dampening mechanisms. The findings highlight the applicability of nonlinear wave models in social conflict analysis and provide insights for early warning systems, targeted policing strategies, and socio-economic interventions. This work contributes to the interdisciplinary field of mathematical social science by extending rogue wave theory into the realm of security studies, offering both theoretical innovation and practical policy relevance.
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