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

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

2010-04-09

arxiv.org/abs/1004.1455v1

Physics

Mathematical Physics

14 pages

Scientific paper

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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