On the Integrability of Non-polynomial Scalar Evolution Equations
نویسندگان
چکیده
منابع مشابه
On the Integrability of Scalar Evolution Equations
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...
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We prove two general results on generalized symmetries for equations of the form ut = um + f(u, u1, . . . , um−1), where f is a formal (differential) power series starting with terms that are at least quadratic. The first result states that any higher order symmetry must be also a differential polynomial if f is a differential polynomial of order less than m − 1. The method is to estimate the o...
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Abstract We prove that arbitrary (non-polynomial) scalar evolution equations of orderm ≥ 7, that are integrable in the sense of admitting the canonical conserved densities ρ, ρ, and ρ introduced in [A.V. Mikhailov, A.B. Shabat and V.V Sokolov “The symmetry approach to the classification of integrable equations” in ‘What is Integrability? edited by V.E. Zakharov (Springer-Verlag, Berlin 1991)], ...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2000
ISSN: 0022-0396
DOI: 10.1006/jdeq.2000.3782