Nonlinear Stability of Field–Wave Configurations in the Locked SU(2) Skyrme Model - Paper 4

This paper establishes nonlinear stability of Field-Wave configurations in the locked SU(2) Skyrme model, proving that these radiation-like excitations are dynamically robust under the full nonlinear dynamics. We prove that for small amplitude ε and perturbation size δ, Field-Wave reference solutions remain O(δ + ε³)-close to the reference trajectory in Sobolev norms on time intervals of length at least c₀/(ε² + δ). The analysis uses quasilinear wave structure, energy estimates, and the cubic nonlinearity structure identified in Paper III. The emergent Maxwell field F_μν(U) is shown to stay close to the ideal Field-Wave Maxwell field over these time scales. These results demonstrate that the Field-Wave/Maxwell sector is not only kinematically present (Paper II) and asymptotically consistent (Paper III), but also nonlinearly metastable under the full SU(2) Skyrme dynamics. This establishes the Field-Wave sector as a dynamically robust emergent sector for radiation-like excitations. This work is part of a program to realize both matter (Skyrmions) and radiation (Maxwell waves) as different configurations of a single continuous SU(2) Skyrme field.