On nonlocal symmetries for the Krichever--Novikov equation
Petr Vojcak
TL;DR
This paper develops new infinite hierarchies of nonlocal symmetries and cosymmetries for the Krichever--Novikov equation by utilizing its fourth-order recursion operator, advancing the understanding of its symmetry structure.
Contribution
It introduces a novel method to generate nonlocal symmetries for the Krichever--Novikov equation using the inverse of its recursion operator.
Findings
Constructed new hierarchies of nonlocal symmetries
Enhanced understanding of the equation's symmetry structure
Provided tools for further integrability analysis
Abstract
We construct new infinite hierarchies of nonlocal symmetries and cosymmetries for the Krichever--Novikov equation using the inverse of the fourth-order recursion operator of the latter.
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