Abstract
This paper analyzes a nonlinear variational wave equation in which the wave speed is a function of the dependent variable. The wave equation arises is a number of different physical contexts and is the simplest example of an interesting class of nonlinear hyperbolic partial differential equations. We describe a blow-up result for the one-dimensional wave equation which shows that smooth solutions break down in finite time. We illustrate this result with some numerical solutions. We also derive a closed system of equations which describe the interaction between the mean field of a solution and oscillations in its spatial derivative.