3 papers
math-ph2016
On the Classifications of Scalar Evolution Equations with Non-constant Separant
Ayşe Hümeyra Bilge, Eti Mizrahi
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 F}/{\partial u_m} w…
nlin.SI2012
A New Graded Algebra Structure on Differential Polynomials: Level Grading and its Application to the Classification of Scalar Evolution Equations in 1+1 Dimension
E. Mizrahi, A. H. Bilge
We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives over the ring $K^{(…
nlin.SI2009
Toward the Classification of Scalar Nonpolynomial Evolution Equations:Polynomiality in Top Three Derivatives
Eti Mizrahi, Ayşe Hümeyra Bilge
We prove that arbitrary (nonpolynomial) scalar evolution equations of order , that are integrable in the sense of admitting the canonical conserved densities $\ro^{(1)}$, $…