On the Lattice Potential KP Equation
Exactly Solvable and Integrable Systems
2020-07-10 v1
Abstract
The paper presents an approach to derive finite genus solutions to the lattice potential Kadomtsev-Petviashvili (lpKP) equation introduced by F.W. Nijhoff, et al. This equation is rederived from compatible conditions of three replicas of the discrete ZS-AKNS spectral problem, which is a Darboux transformation of the continuous ZS-AKNS spectral problem. With the help of these links and by means of the so called nonlinearization technique and Liouville platform, finite genus solutions of the lpKP equation are derived. Semi-discrete potential KP equations with one and two discrete arguments, respectively, are also discussed.
Cite
@article{arxiv.2007.04721,
title = {On the Lattice Potential KP Equation},
author = {Cewen Cao and Xiaoxue Xu and Da-jun Zhang},
journal= {arXiv preprint arXiv:2007.04721},
year = {2020}
}
Comments
21 pages