We consider the following degenerate half-wave equation on the one-dimensional torus:
We show that, on a large time interval, the solution may be approximated by the solution of a completely integrable system—the cubic Szegő equation. As a consequence, we prove an instability result for large norms of solutions of this wave equation.
"Effective integrable dynamics for a certain nonlinear wave equation." Anal. PDE 5 (5) 1139 - 1155, 2012. https://doi.org/10.2140/apde.2012.5.1139