Burgers equation: steepening waveform develops a shock discontinuity
t = 0.000 max gradient: —
Burgers' equation ∂u/∂t + εu∂u/∂x = ν∂²u/∂x² models nonlinear wave steepening. Characteristics converge where high-amplitude regions move faster, forming a shock. Viscosity regularizes the discontinuity into a steep but smooth front. The Cole-Hopf transformation renders it exactly solvable.