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.