Analytic Lyapunov exponents in a classical nonlinear field equation

It is shown that the nonlinear wave equation Εt2φ-Εx2φ-μ0Εx(Εxφ)0=0, which is the continuum limit of the Fermi-Pasta-Ulam β model, has a positive Lyapunov exponent λ1, whose analytic energy dependence is given. The result (a first example for field equations) is achieved by evaluating the lattice-spacing dependence of λ1 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. © 2000 The American Physical Society.