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 i...

Direct reductions of partial diierential equations to systems of ordinary diierential equations are in one-to-one correspondence with compatible diierential constraints. The diierential constraint method is applied to prove that a parabolic evolution equation admits innnitely many characteristic second order reductions, but admits a non-characteristic second order reduction if and only if it is...