Solutions Classification to the Extended Reduced Ostrovsky Equation

Details Solutions Classification to the Extended Reduced Ostrovsky Equation Solutions Classification to the Extended Reduced Ostrovsky Equation

2008-10-26

arxiv.org/abs/0810.4684v1

SIGMA 4 (2008), 073, 19 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2008.073

An alternative to the Parkes' approach [SIGMA 4 (2008) 053, arXiv:0806.3155] 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 the above mentioned Parkes' paper.

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