PERIODIC BENJAMIN-ONO EQUATION WITH DISCRETELAPLACIAN AND 2D-TODA HIERARCHY

摘要

We study the relation between the periodic Benjamin-Ono equation with dis-crete Laplacian and the two-dimensional-Toda hierarchy. We introduce the tau-functions τ± (z) for the periodic Benjamin-Ono equation, construct two families of integrals of motion {M_1, M_2, ··· }, {M_1, M_2, ··· }, 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.