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arXiv · 1004.1455

Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda Hierarchy

Jun'ichi Shiraishi·Yohei Tutiya
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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.

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Jun'ichi Shiraishi, Yohei Tutiya. 2010-04-09. Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda Hierarchy. https://doi.org/10.1142/9789814324373_0018

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