Nonlinear Scalar Interactions in the EMDrive: Petiau's Elliptic-Function Approach

The EMDrive, a controversial electromagnetic propulsion concept, challenges momentum conservation in standard Maxwell electrodynamics. We propose a beyond-Maxwell framework by coupling the electromagnetic field to a light scalar field, inspired by axion-like particle models and effective field theory. Using Guy Petiau's 1958 elliptic-function solutions for nonlinear wave equations, we construct exact cavity modes and combine them via Jacobi addition theorems. These nonlinear modes produce an asymmetric momentum flux, suggesting a theoretical pathway for EMDrive thrust. We compute the stress-tensor asymmetry numerically and show that while standard axion-like particles yield negligible effects, light scalars beyond current constraints could produce measurable thrust. The framework provides testable predictions connecting EMDrive physics to dark matter searches.