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SIGMA 4 (2008), 073, 19 pages arXiv:0810.4684
https://doi.org/10.3842/SIGMA.2008.073
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
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].
Key words:
reduced Ostrovsky equation; mechanical analogy; phase plane; periodic waves; solitary waves, compactons.
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References
- Parkes E.J., Periodic and solitary travelling-wave solutions of an
extended reduced Ostrovsky equation, SIGMA 4 (2008),
053, 17 pages, arXiv:0806.3155.
- Morrison A.J., Parkes E.J.,
The N-soliton solution of the modified generalised Vakhnenko equation
(a new nonlinear evolution equation),
Chaos Solitons Fractals 16 (2003), 13-26.
- Li J.-B.,
Dynamical understanding of loop soliton solution for several nonlinear wave equations,
Sci. China Ser. A 50 (2007), 773-785.
- Stepanyants Y.A., On stationary solutions of the reduced Ostrovsky
equation: Periodic waves, compactons and compound solitons,
Chaos Solitons Fractals 28 (2006), 193-204.
- Ostrovsky L.A., Nonlinear internal waves in a rotating ocean,
Okeanologiya 18 (1978), 181-191 (Engl.
transl: Oceanology 18 (1978), 119-125).
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