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arXiv · 2409.19530

On Tautological Flows of Partial Difference Equations

Zhonglun Cao·Si-Qi Liu·Youjin Zhang
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Abstract

We propose a new analyzing method, which is called the tautological flow method, to analyze the integrability of partial difference equations (P$\Delta$Es) based on that of partial differential equations (PDEs). By using this method, we prove that the discrete $q$-KdV equation is a discrete symmetry of the $q$-deformed KdV hierarchy and its bihamiltonian structure, and we also demonstrate how to directly search for continuous symmetries and bihamiltonian structures of P$\Delta$Es by using the approximated tautological flows and their quasi-triviality transformation.

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Zhonglun Cao, Si-Qi Liu, Youjin Zhang. 2024-09-29. On Tautological Flows of Partial Difference Equations. https://arxiv.org/abs/2409.19530

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