This considers useful nonlinear PDE systems whose symmetry group contains a general solution of a linear PDE, but in one fewer space dimensions.

The systems include:

• A class of reaction-diffusion equations in n dimensions, giving the only known exact solution in combustion with Arrhenius (Gibbs-Boltzmann) combustion term,
• A complex-valued Madelüng fluid picture of quantum mechanics, that reduces to the Schrödinger equation by the Hopf-Cole transformation of a Burgers fluid. This provides a dynamical model of the quantum measurement problem.
• 2D electron gas diffusion with reciprocal diffusivity D=1/u.