An integrable hierarchy without a recursion operator

Author:

Sergei Sakovich

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph)

journal:

Nonlinear Phenom. Complex Syst. 26 (2023) 131-138

date:

2023-04-29 16:00:00

Abstract

We study the Lax integrability of a nonlinear system of two coupled second-order evolution equations introduced by Ibragimov and Shabat. For this system we find a zero-curvature representation with an essential parameter, construct an infinite integrable hierarchy which the system belongs to, and show that this hierarchy does not possess a recursion operator.

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