Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda Hierarchy
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 taupm(z) for the periodic Benjamin-Ono equation, construct two families of integrals of motion M1,M2,cdots, overlineM1,overlineM2,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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