Fractional Optical Solitons and Fractional Noether’s Theorem with Ortigueira’s Centered DerivativesReport as inadecuate




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This paper shows that the centeredfractional derivatives introduced by Manuel Duarte Ortigueira in 2006 areuseful in the description of optical solitons. It is shown that we canconstruct a fractional extension of the nonlinear Schrödinger NLS equationwhich incorporates Ortigueira’s derivatives and has soliton solutions. It isalso shown that this fractional NLS equation has a Lagrangian density and canbe derived from a variational principle. Finally, a fractional extension ofNoether’s theorem is formulated to determine the conserved quantitiesassociated to the invariances of the action integral under infinitesimaltransformations.

KEYWORDS

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

Cite this paper

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.





Author: Jorge Fujioka1, Manuel Velasco1, Argel Ramírez2

Source: http://www.scirp.org/



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