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DCDS

Considered herein is an initial-value problem for the Ostrovsky equation
that arises in modelling the unidirectional propagation of long waves in a
rotating homogeneous incompressible fluid. Nonlinearity and dispersion are
taken into account, but dissipation is ignored. Local- and global-in-time
solvability is investigated. For the case of positive dispersion a
fundamental solution of the Cauchy problem for the linear equation is
constructed, and its asymptotics is calculated as $t\rightarrow \infty, x/t=$const. For the nonlinear problem solutions are constructed in the
form of a series and the analogous long-time asymptotics is obtained.

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