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Solutions classification to the extended reduced Ostrovsky equation. (English) Zbl 1169.35378
Summary: An alternative to the Parkes’ approach [E. J. Parkes, SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 053, 17 pages, electronic only (2008; Zbl 1147.35101)] 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 [Parkes, loc. cit.].
MSC:
35Q58Other completely integrable PDE (MSC2000)
35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form
35Q51Soliton-like equations
35B10Periodic solutions of PDE