Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 073, 19 pages      arXiv:0810.4684

Solutions Classification to the Extended Reduced Ostrovsky Equation

Yury A. Stepanyants
Australian Nuclear Science and Technology, Organisation PMB 1, Menai (Sydney), NSW, 2234, Australia

Received July 14, 2008, in final form October 13, 2008; Published online October 26, 2008

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].

Key words: reduced Ostrovsky equation; mechanical analogy; phase plane; periodic waves; solitary waves, compactons.

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