Reduction of differential Fay identity and integral of motions of algebro-geometric solutions

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  • 微分型Fay 恒等式の縮約と運動の積分のテータ関数解における値について
  • ビブンガタ Fay コウ トウシキ ノ シュクヤク ト ウンドウ ノ セキブン ノ テータ カンスウカイ ニ オケル アタイ ニ ツイテ

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Abstract

IIn this note, we discuss polynomial solutions of Periodic Benjamin-Ono equation with discrete Laplacian. The integral of motions of these solutions are written by symmetric functions of soliton length, which obviously correspond to the eigenvalues of Macdonald q-difference operators. The purpose is to show that the so-called algebro-geometric solutions of reduced differential Fay identity degenerate into these polynomial solutions.

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