15 citations · 83 across the 35 of their papers we have counts for
4 papers · 1 filter
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^{(…
On the Classification of Fifth Order Quasi-linear Non-constant Separant Scalar Evolution Equations of the KdV-type
Gulcan Ozkum, Ayse H. Bilge
Fifth order, quasi-linear, non-constant separant evolution equations are of the form u_t=A\frac{\partial^5 u}{\partial x^5}+\tilde{B}, where A and \tilde{B} are functions of x, t,…
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 $\ro^{(1)}$, $…
On the Classification of Scalar Non-Polynomial Evolution Equations: Quasilinearity
Ayse Humeyra Bilge
We prove that, for , scalar evolution equations of the form which admit a nontrivial conserved density of order are linear in . The existe…