On the interaction of solitary waves of flexure in elastic rods.

*(English)*Zbl 0849.73029Summary: A numerical study is made to determine whether the partial differential equations governing planar, twist-free motions in a theory of the dynamics of elastic rods are completely integrable in the sense of soliton theory. The theory in which the equations arise is due to Kirchhoff and Clebsch and is complete to within an error of order two in an appropriate dimensionless measure of thickness and strain. A recently developed energy-preserving finite-difference scheme is employed to determine the consequences of the interaction of solitary traveling waves, which in the present twist-free case, are loops traveling at constant speed. It is found that the change induced in such a loop-wave upon collision with another is more than a shift in phase.

Reviewer: Reviewer (Berlin)

##### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

74S20 | Finite difference methods applied to problems in solid mechanics |

##### Keywords:

completely integrable equations; energy-preserving finite-difference scheme; twist-free case
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\textit{B. D. Coleman} and \textit{J. M. Xu}, Acta Mech. 110, No. 1--4, 173--182 (1995; Zbl 0849.73029)

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##### References:

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