Abstract
In 1991, Goldstein and Petrich showed that the dynamics of a curve in a plane is governed geometrically by the modified KdV (mKdV) hierarchy. In this paper, we show a way of utilizing their new tool of the soliton approach to analyse the nonlinear dynamics of elastic rods. Considering the stretching effect of a narrow rod, nonlinear dynamics is studied by using exact soliton solutions of the mKdV equation, such as one soliton and breather soliton solutions. The metric of the rod which represents the stretching effect is explicitly given by perturbation analyses, and it is shown that an initial tension of the rod plays an important role in forming solitons in the rod.
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