On stationary solutions of the reduced Gardner–Ostrovsky equation
Article
Article Title | On stationary solutions of the reduced Gardner–Ostrovsky equation |
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Article Category | Article |
Authors | Obregon, Maria (Author) and Stepanyants, Yury (Author) |
Journal Title | Discontinuity, Nonlinearity and Complexity |
Journal Citation | 3 (4), pp. 445-456 |
Number of Pages | 12 |
Year | 2014 |
Place of Publication | St. Louis,MI, USA |
Digital Object Identifier (DOI) | https://doi.org/10.5890/DNC.2014.12.007 |
Abstract | The detailed analysis of stationary solutions of the reduced Gardner–Ostrovsky (GO) equation is presented. The GO equation is the popular model for the description of large-amplitude internal oceanic waves affected by Earth’s rotation. Its reduced version in which the small-scale dispersion is neglected is used when very long internal waves are considered. The equation is also applicable to other types of nonlinear waves in various media (plasma, optical media, relaxing media, etc.) when the large-scale dispersion plays a dominant role in comparison with the small-scale dispersion. Balancing the nonlinear effect such dispersion gives rise to existence of stationary waves, both periodic and non-periodic. It is shown that only smooth periodic waves make physical sense. Systematic analysis of stationary solutions to the GO equation and their categorisation is presented. |
Keywords | Gardner–Ostrovsky equation; periodic waves; stationary solution; rotational dispersion; oceanic waves |
ANZSRC Field of Research 2020 | 401207. Fundamental and theoretical fluid dynamics |
370803. Physical oceanography | |
490109. Theoretical and applied mechanics | |
Byline Affiliations | University of Malaga, Spain |
School of Agricultural, Computational and Environmental Sciences | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q2vxq/on-stationary-solutions-of-the-reduced-gardner-ostrovsky-equation
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