Author(s)

Jorge Fujioka¹, Manuel Velasco¹, Argel Ramírez²

¹Instituto de Física, Departamento De Física-Química, Universidad Nacional Autónoma de México, México D.F., México.
¹nstituto de Física, Departamento De Física-Química, Universidad Nacional Autónoma de México, México D.F., México.
²Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México, México D.F., México.

This paper shows that the centered fractional derivatives introduced by Manuel Duarte Ortigueira in 2006 are useful in the description of optical solitons. It is shown that we can construct a fractional extension of the nonlinear Schrödinger (NLS) equation which incorporates Ortigueira’s derivatives and has soliton solutions. It is also shown that this fractional NLS equation has a Lagrangian density and can be derived from a variational principle. Finally, a fractional extension of Noether’s theorem is formulated to determine the conserved quantities associated to the invariances of the action integral under infinitesimal transformations.

Fractional Derivatives, Centered Derivatives, Noether’s Theorem, Ortigueira, Optical Solitons

Fujioka, J. , Velasco, M. and Ramírez, A. (2016) Fractional Optical Solitons and Fractional Noether’s Theorem with Ortigueira’s Centered Derivatives. Applied Mathematics, 7, 1340-1352. doi: 10.4236/am.2016.712118.