Direct Reduction and Differential Constraints

@inproceedings{Olver1994DirectRA,
  title={Direct Reduction and Differential Constraints},
  author={Peter J. Olver},
  year={1994}
}
Direct reductions of partial differential equations to systems of ordinary differential equations are in one-to-one correspondence with compatible differential constraints. The differential constraint method is applied to prove that a parabolic evolution equation admits infinitely many characteristic second order reductions, but admits a noncharacteristic second order reduction if and only if it is linearizable. 
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