Wave-breaking and generic singularities of nonlinear hyperbolic equations

Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power laws derived from general arguments and the singular behavior of solutions of nonlinear hyperbolic differential equations are in excellent agreement with the numerical results. This shows the power of the analysis by methods using generic concepts of nonlinear science.