Jet bundle formalism towards the extension of the stretched rope equation

In this paper, based upon a jet bundle formalism, we investigate the connection and the curvature associated to the stretched rope equation. Following the prolongation structure analysis due to Wahlquist and Estabrook combined to Cartan-Ehresmann connection with structure group SL(3,R), we derive an interesting coupled system dubbed as the two-component stretched rope equation which physically and geometrically arises from the curve motion flow in Euclidean space.