Browsing by Author "Mizrahi, Eti"
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'Level grading' a new graded algebra structure on differential polynomials: application to the classification of scalar evolution equations
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 Cinfinity functions of x t u u(1) ... u(k) where . This grading has the property that the total derivative and the integration by parts with respect to x are filtered algebra maps. In addition if u satisfies the evolution equation u(j) = F[u] where F is a polynomial of order m = k + p and of level p then the total derivative with respect to t Dt is ...

On the classification of scalar evolution equations with nonconstant separant
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 derivative(m)u/partial derivative x(m). As an integrability test we use the formal symmetry method of MikhailovShabatSokolov which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives ...