Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda Hierarchy
Mathematical Physics
2017-08-23 v1 math.MP
Quantum Algebra
Abstract
We study the relation between the periodic Benjamin-Ono equation with discrete Laplacian and the two dimensional Toda hierarchy. We introduce the tau-functions tau_pm(z) for the periodic Benjamin-Ono equation, construct two families of integrals of motion {M_1,M_2,cdots}, {overline{M}_1,overline{M}_2,cdots}, and calculate some examples of the bilinear equations using the Hamiltonian structure. We confirmed that some of the low lying bilinear equations agree with the ones obtained from a certain reduction of the 2D Toda hierarchy.
Keywords
Cite
@article{arxiv.1004.1455,
title = {Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda Hierarchy},
author = {Jun'ichi Shiraishi and Yohei Tutiya},
journal= {arXiv preprint arXiv:1004.1455},
year = {2017}
}
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14 pages