Burgers Equation

For conservation laws in general, there’s the implicit solution of u = F(x - ut). It’s surprisingly useful for quick and dirty “exact” solutions to a lot of problems. In particular inviscid Burgers’ equation with initial values becomes trivial to code up.

For example, in Python it would be literally one line:

return optimize.fsolve(lambda u: u - self.u0(x - u*t), 1)

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