A KP-mKP Hierarchy via Operators with Two Derivations
Exactly Solvable and Integrable Systems
2023-11-15 v2
Abstract
By using pseudo-differential operators containing two derivations, we extend the Kadomtsev-Petviashvili (KP) hierarchy to a certain KP-mKP hierarchy. For the KP-mKP hierarchy, we obtain its B\"{a}cklund transformations, bilinear equations of Baker-Akhiezer functions and Hirota equations of tau functions. Moreover, we show that this hierarchy is equivalent to a subhierarchy of the dispersive Whitham hierarchy associated to the Riemann sphere with its infinity point and one movable point marked.
Cite
@article{arxiv.2311.07341,
title = {A KP-mKP Hierarchy via Operators with Two Derivations},
author = {Lumin Geng and Jianxun Hu and Chao-Zhong Wu},
journal= {arXiv preprint arXiv:2311.07341},
year = {2023}
}