The Shock Never Left the Starting Line — Where Conservative and Primitive Forms Split
·8 min read
Flux-form Burgers returns shock speed 0.5006. Writing velocity times a gradient returns 0.0000, and an eightfold grid still settles near 0.639.
When Characteristics Collide, a Shock Is Born — Burgers and the (x,t) Plane
·6 min read
A sine of amplitude 0.35 and wavenumber 1 breaks at t* ≈ 0.455 when characteristics cross, and the weak solution cuts that fold with one line.