Periodic ILW equation with discrete Laplacian
Exactly Solvable and Integrable Systems
2015-05-13 v1 Pattern Formation and Solitons
Abstract
We study an integro-differential equation which generalizes the periodic intermediate long wave (ILW) equation. The kernel of the singular integral involved is an elliptic function written as a second order difference of the Weierstrass zeta-function. Using Sato's formulation, we show the integrability and construct some special solutions. An elliptic solution is also obtained. We present a conjecture based on a Poisson structure that it gives an alternative description of this integrable hierarchy. We note that this Poisson algebra in turn is related to a quantum algebra related with the family of Macdonald difference operators.
Cite
@article{arxiv.0904.2644,
title = {Periodic ILW equation with discrete Laplacian},
author = {J. Shiraishi and Y. Tutiya},
journal= {arXiv preprint arXiv:0904.2644},
year = {2015}
}
Comments
17 pages. To appear in J. Phys. A: Math. Theor