On the Integrability of Scalar Evolution Equations

  title={On the Integrability of Scalar Evolution Equations},
  author={Jan A. Sanders and Jing Ping Wang},
This paper was motivated by the observation that after quickly finding a number of hierarchies (mKdV, Sawada-Kotera, Kaup-Kuperschmidt) soon after finding that KdV was integrable, nothing more was found for polynomial scalar evolution equations linear in the highest order derivative. In this paper we prove that under some mild conditions on the equations one can put a uniform bound on the order of the recursion operator of any such hierarchy. We do this using the symbolic method, introduced by… CONTINUE READING
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On a sequence of polynomials

Frits Beukers
Journal of Pure and Applied Algebra, • 1997

Three basic conservation laws of a class of evolution equations

M. Z. Qin, G. Z. Tu
Acta Mathematicæ Applicatæ Sinica, • 1982

The invariant groups and conservation laws of nonlinear evolution equations–an approach of symmetric function

G. Z. Tu, M. Z. Qin
Scientia Sinica, • 1981

Asymptotic behaviour of the resolvent of Sturm – Liouville equations and the algebra of the Korteweg – de Vries equations

G. Z. Tu
Russian Math . Surveys • 1975

Dikii. Asymptotic behaviour of the resolvent of Sturm–Liouville equations and the algebra of the Korteweg–de Vries equations

L.A.I.M. Gel’fand
Russian Math. Surveys, • 1975

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