Trans-resonant evolution of wave singularities and vortices

Nonlinear resonant wave phenomena are treated. It is assumed that near and at the resonance first-order linear terms in perturbed wave equations annihilate each other. As a result, the perturbed wave equations reduce to basic highly nonlinear ordinary differential equation or the basic algebraic equation for traveling waves. These equations determine the evolution of smooth waves into shock waves. Then the jump curls and eventually breaks, nucleating drops, bubbles or vortices