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Approximate Analytical and Numerical Solutions of the Stationary Ostrovsky Equation
Author(s) -
Gilman O. A.,
Grimshaw R.,
Stepanyants Yu. A.
Publication year - 1995
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1995951115
Subject(s) - dispersion (optics) , computation , mathematics , nonlinear system , rotation (mathematics) , mathematical analysis , korteweg–de vries equation , numerical analysis , classical mechanics , physics , geometry , quantum mechanics , algorithm
Approximate stationary solutions of the Ostrovsky equation describing long weakly nonlinear waves in a rotating liquid are constructed. These solutions may be regarded as a periodic sequence of arcs of parabolas containing Korteweg‐de Vries solitons at the junctures. Results of numerical computations of the dynamics of the approximate solutions obtained from the nonstationary Ostrovsky equation are presented. It is found that, in the presence of negative dispersion, the shape of a stationary wave is well predicted by the approximate theory, whereas the calculated wave velocity differs slightly from the theoretical value. The stationary solutions in media with positive dispersion are evidently unstable (at least for sufficiently strong rotation), and numerical computations demonstrate a complicated picture of nonstationary destruction.