Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 091, 12 pages      arXiv:2106.03835      https://doi.org/10.3842/SIGMA.2021.091
Contribution to the Special Issue on Mathematics of Integrable Systems: Classical and Quantum in honor of Leon Takhtajan

Negative Times of the Davey-Stewartson Integrable Hierarchy

Andrei K. Pogrebkov ab
a) Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b) Skolkovo Institute of Science and Technology, Moscow, Russia

Received June 08, 2021, in final form October 01, 2021; Published online October 12, 2021

Abstract
We use example of the Davey-Stewartson hierarchy to show that in addition to the standard equations given by Lax operator and evolutions of times with positive numbers, one can consider time evolutions with negative numbers and the same Lax operator. We derive corresponding Lax pairs and integrable equations.

Key words: commutator identities; integrable hierarchies; reductions.

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