Effective integrable dynamics for a certain nonlinear wave equation

Abstract

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 H s norms of solutions of this wave equation.However, Equation ( 1) is a nondispersive equation.Indeed, it is equivalent to the systemMSC2010: 35B34, 35B40, 37K55.

Locations

• Analysis & PDE - View - PDF
• Project Euclid (Cornell University) - View - PDF