Year: 2018
Type: article
Abstract: It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symmetries and infinite series of the local conservation laws. In the literature, we can find several methods for constructing recursion operators, some of them use the Hamiltonian approach and the others are based on the Lax representation of the equation. In the present article we discuss an alternative method, suggested in Habibullin and Khakimova (2018 Theor. Math. Phys . 196 1200–16), which is connected only with the first several generalized symmetries of the given equation. Efficiency of the method is illustrated with the examples of Korteweg–de Vries, Krichever–Novikov and Kaup–Kupershmidt equations and discrete autonomous and non-autonomous models.
Authors: I T Habibullin, A R Khakimova
Institutions: Russian Academy of Sciences, Bashkir State University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2798809271