  It is shown that the nonlinear wave equation $\partial_t^2\phi - \partial^2_x
\phi -\mu_0\partial_x(\partial_x\phi)^3 =0$, which is the continuum limit of
the Fermi-Pasta-Ulam (FPU) beta model, has a positive Lyapunov exponent
lambda_1, whose analytic energy dependence is given. The result (a first
example for field equations) is achieved by evaluating the lattice-spacing
dependence of lambda_1 for the FPU model within the framework of a Riemannian
description of Hamiltonian chaos. We also discuss a difficulty of the
statistical mechanical treatment of this classical field system, which is
absent in the dynamical description.
