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arXiv · 2201.03205

A class of extended high-dimensional nonisospectral KdV hierarchies and symmetry

Haifeng Wang·Yufeng Zhang·Binlu Feng
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Abstract

We construct a new class of N-dimensional Lie algebras and apply them to integrable systems. In this paper, we obtain a nonisospectral KdV integrable hierarchy by introducing a nonisospectral spectral problem. Then, a coupled nonisospectral KdV hierarchy is deduced by means of the corresponding higher-dimensional loop algebra. It follows that the K symmetries, {\tau} symmetries and their Lie algebra of the coupled nonisospectral KdV hierarchy are investigated. The bi-Hamiltonian structures of the both resulting hierarchies are derived by using the trace identity. Finally, we derive a multi-component nonisospectral KdV hierarchy related to the N-dimensional loop algebra, which generalizes the coupled results to an arbitrary number of components.

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Haifeng Wang, Yufeng Zhang, Binlu Feng. 2022-01-10. A class of extended high-dimensional nonisospectral KdV hierarchies and symmetry. https://arxiv.org/abs/2201.03205

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