TITLE:
Fractional Optical Solitons and Fractional Noether’s Theorem with Ortigueira’s Centered Derivatives
AUTHORS:
Jorge Fujioka, Manuel Velasco, Argel Ramírez
KEYWORDS:
Fractional Derivatives, Centered Derivatives, Noether’s Theorem, Ortigueira, Optical Solitons
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.12,
July
26,
2016
ABSTRACT: 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.