Solutions classification to the extended reduced Ostrovsky equation

Stepanyants, Yury A. (2008) Solutions classification to the extended reduced Ostrovsky equation. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 4.

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Abstract

An alternative to the Parkes’ approach [SIGMA 4 (2008), 053, 17 pages] is suggested for the solutions categorization to the extended reduced Ostrovsky equation (the exROE in Parkes’ terminology). The approach is based on the application of the qualitative theory of differential equations which includes a mechanical analogy with the point particle motion in a potential field, the phase plane method, analysis of homoclinic trajectories and the like. Such an approach is seemed more vivid and free of some restrictions contained in [SIGMA 4 (2008), 053, 17 pages].


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: The authors retain ownership of the copyright with respect to their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.
Depositing User: Assoc Prof Yury Stepanyants
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 30 Jan 2010 07:39
Last Modified: 02 Jul 2013 23:24
Uncontrolled Keywords: reduced Ostrovsky equation; mechanical analogy; phase plane; periodic waves; solitary waves; compactons
Fields of Research (FOR2008): 01 Mathematical Sciences > 0105 Mathematical Physics > 010599 Mathematical Physics not elsewhere classified
01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.3842/SIGMA.2008.073
URI: http://eprints.usq.edu.au/id/eprint/5725

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