Departmental Seminar

Conditionally integrable nonlinear PDE models

Professor Philip Broadbridge
La Trobe university

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.

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