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KIAM Preprint № 68, Moscow, 2005
Authors: Bruno A. D., Gashenenko I.N.
Simple Finite Solutions to the N.Kowalewski Equations
Abstract:
Earlier we have found all 24 families of power-logarithmic expansions in p of solutions to the N.Kowalewski system of equations, describing motions of a rigid body with a fixed point in the case B ≠ C, x0 ≠ 0, y0=z0=0. Among them, 10 families have p → 0 (tails) and 14 families have p → ∞ (heads). To find all finite expansions we check each pair a tail and a head: can it give a finite expansion or it cannot By this approach we find all finite solutions to the N.Kowalewski equations, in particular, all 7 known and 5 new. All new solutions are complex. We also prove the absente of other solution which is the finite sum of rational powers of p.
Publication language: russian
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Bruno Alexander Dmitrievich,  orcid.org/0000-0002-7465-1258KIAM RAS
  • Gashenenko I.N.