The reciprocal link between the reduced Ostrovsky equation and the
A2(2)β two-dimensional Toda system is used to construct the N-soliton
solution of the reduced Ostrovsky equation. The N-soliton solution of the
reduced Ostrovsky equation is presented in the form of pfaffian through a
hodograph (reciprocal) transformation. The bilinear equations and the
Ο-function of the reduced Ostrovsky equation are obtained from the period
3-reduction of the Bββ or Cββ two-dimensional Toda system,
i.e., the A2(2)β two-dimensional Toda system. One of Ο-functions of
the A2(2)β two-dimensional Toda system becomes the square of a pfaffian
which also become a solution of the reduced Ostrovsky equation. There is
another bilinear equation which is a member of the 3-reduced extended BKP
hierarchy. Using this bilinear equation, we can also construct the same
pfaffian solution.Comment: 16 pages, several typos were correcte