Solutions Classification to the Extended Reduced Ostrovsky Equation
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].
- Publication:
-
SIGMA
- Pub Date:
- October 2008
- DOI:
- 10.3842/SIGMA.2008.073
- arXiv:
- arXiv:0810.4684
- Bibcode:
- 2008SIGMA...4..073S
- Keywords:
-
- reduced Ostrovsky equation;
- mechanical analogy;
- phase plane;
- periodic waves;
- solitary waves;
- compactons;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics
- E-Print:
- Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/