In this study, we establish a link of the coupled dispersionless (CD) equations system with the motion of Bertrand curve pairs. Moreover, we find the Lax equations that provide the integrability of these equations. By taking an appropriate choice of variables we show the link of the short pulse (SP) equation with the motion of Bertrand curve pairs via the reciprocal (hodograph) transformation. Finally, we prove that the conserved quantity of the corresponding coupled dispersionless equations obtained from each of these curve pairs is constant.
"Forming coupled dispersionless equations of families of Bertrand curves,"
Turkish Journal of Mathematics: Vol. 47:
1, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss1/6