Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy
Xian-long Sun, Da-jun Zhang, Xiao-ying Zhu, Deng-yuan Chen
TL;DR
This paper constructs two sets of symmetries for the differential-difference Kadomstev-Petviashvili hierarchy using non-isospectral flows, revealing an infinite-dimensional Lie algebra structure.
Contribution
It introduces a novel method to generate symmetries for the hierarchy and characterizes their algebraic structure.
Findings
Symmetries form an infinite-dimensional Lie algebra.
Two sets of symmetries are constructed using non-isospectral flows.
The algebraic structure of the symmetries is explicitly described.
Abstract
By introducing suitable non-isospectral flows we construct two sets of symmetries for the isospectral differential-difference Kadomstev-Petviashvili hierarchy. The symmetries form an infinite dimensional Lie algebra.
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