  We study traveling wave solutions of the nonlinear variational wave equation.
In particular, we show how to obtain global, bounded, weak traveling wave
solutions from local, classical ones. The resulting waves consist of monotone
and constant segments, glued together at points where at least one one-sided
derivative is unbounded. Applying the method of proof to the Camassa--Holm
equation, we recover some well-known results on its traveling wave solutions.
