We consider fully nonlinear gauge invariant evolution of the plane wave. Although the plane wave does not decay at infinity, by an elementary and simple argument we find an extremely smooth solution which has an explicit expression. Additionally, we study the global behavior of the solution from its representation.
"Fully nonlinear gauge invariant evolution of the plane wave." Differential Integral Equations 21 (9-10) 851 - 858, 2008. https://doi.org/10.57262/die/1356038589