Spatio-temporal chaos and intermittency in a 1-dimensional energy-conserving coupled map lattice

The Klein—Gordon equation with cubic nonlinearity (the φ4 equation) is considered and an energy-conserving difference scheme is proposed for its solution. The scheme, extended to finite time increments and spacing, is then used to define a coupled map lattice for which an energy-like functional is conserved. The case of linear instability of the vacuum state is considered when this energy is not positive definite and found to lead, under certain additional conditions, to spatio-temporal chaos. The statistical properties of this type of solution such as probability densities and correlation functions are calculated. Strong intermittency, whereby the process wanders between two sub-manifolds, is found and studied in detail.