APPROXIMATE ANALYTICAL AND NUMERICAL-SOLUTIONS OF THE STATIONARY OSTROVSKY EQUATION

Approximate stationary solutions of the Ostrovsky equation describing long weakly nonlinear waves in a rotating liquid are constructed. Thes e solutions may be regarded as a periodic sequence of arcs of parabola s containing Kortewegde Vries solitons at the junctures. Results of nu merical computations of the dynamics of the approximate solutions obta ined from the nonstationary Ostrovsky equation are presented. It is fo und that, in the presence of negative dispersion, the shape of a stati onary wave is well predicted by the approximate theory, whereas the ca lculated wave velocity differs slightly from the theoretical value, Th e stationary solutions in media with positive dispersion are evidently unstable (at least for sufficiently strong rotation), and numerical c omputations demonstrate a complicated picture of nonstationary destruc tion.