In this paper We show We obtain generalization Example of mKdV is explicite given. curvature satisfy soliton equations [Has], H. Hasimoto A soliton on a vortex filament, J. Fluid Mech. vol. 51, part 3, pp. 477-485, (1972). [DS] A. Doliwa, P.M. Santini, An elementary geometric characterization of the integrable motions of a curve, Phys. Lett. A, 185, 337-, 1994. [NSW], K. Nakayama, H. Segur, M. Wadati, Integrability and the Motion of Curves, Phys. Rev, Lett., vol 69, n. 18, 1992. [Lak1] M. Lakshmanan, On the Geometrical Interpretation of Solitons, Phys. Lett. vol. 64A,n. 4, 354-, 1977. [Lak2] M. Lakshmanan, Rigid body motions, space curves, prolongation structures, fiber bundles and solitons J. Math. Phys. 20(8), 1667-, 1979 [GolPet] R. E. Goldstein, D. M. Petrich, The Korteweg-de Vries Hierarchy as Dynamics of Closed Curves in the Plane Phys. Rev, Lett., vol 67, n. 23, 3203-, 1992.