Constructive and destructive interferences in nonlinear hyperbolic equations Summary: This article introduces a physically realistic model for explaining how electromagnetic waves can be internally generated propagate and interact in strongly magnetized plasmas or in nuclear magnetic resonance experiments. It studies high frequency solutions of nonlinear hyperbolic equations for time scales at which dispersive and nonlinear effects can be present in the leading term of the solutions. It explains how the produced waves can accumulate during long times to produce constructive and destructive interferences which in the above contexts are part of turbulent effects.