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'Level grading' a new graded algebra structure on differential polynomials: application to the classification of scalar evolution equations
(IOP Publishing Ltd, 2013)
We define a new grading which we call the 'level grading' on the algebra of polynomials generated by the derivatives u(k+i) over the ring K-(k) of C-infinity functions of x t u u(1) ... u(k) where . This grading has the ...
On the classification of scalar evolution equations with non-constant separant
(IOP Publishing Ltd, 2017)
The ` separant' of the evolution equation u(t) = F where F is some differentiable function of the derivatives of u up to order m is the partial derivative partial derivative F/partial derivative u(m) where um u(m) = partial ...