Abstract
A new approach to numerical integration of nonlinear PDE with two resonantly-coupling bands of slowly evolving modes, originated in the problem's symmetry, is developed. The bands are centered around a certain finite wavenumber and wavenumber equal to zero, respectively, that gives rise to a complicated spatiotemporal behaviour of solutions. The approach is based on reduction of the problem to a truncated set of coupled equations for Fourier-transforms of the order parameter supplemented, by exclusion of the slaved mode. Though the basic equation is stiff, an explicit time marching by Runge-Kutta method with some techniques is successfully performed. Application of the approach to the particular equation governing seismic waves yields solutions that display a new type of turbulence.
