Toward the Classification of Scalar Nonpolynomial Evolution Equations: Polynomiality in Top Three Derivatives
We prove that arbitrary (nonpolynomial) scalar evolution equations of order m ≥ 7 , that are integrable in the sense of admitting the canonical conserved densities (1), (2) , and (3) introduced in [ 1], are polynomial in the derivatives um− i for i = 0, 1, 2. We also introduce a grading in the algebra of polynomials in uk with k ≥ m − 2 over the ring of functions in x, t, u, … , um−3 and show that integrable equations are scale homogeneous with respect to this grading.
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Document Type: Research Article
Affiliations: Istanbul Technical University
Publication date: October 1, 2009