The inviscid Burgers equation ut + u·ux = 0 models nonlinear advection without diffusion — the prototype for shock formation. Each point of the wave moves at its own speed u, so regions where u decreases in x experience characteristic convergence. When characteristics cross, the smooth solution ceases to exist and a shock discontinuity forms. The breaking time t* = −1/min(∂u/∂x) is set by the steepest downslope. The lower panel shows characteristic lines in (x,t) space; their crossing marks the birth of the shock.