Fractional Noether´s Theorem and Fractional Optical Solitons with Ortigueira´s and Grünwald-Letnikov´s Derivatives | Chapter 07 | Recent Recent Advances in Mathematical Research and Computer Science Vol. 9

 This work demonstrates how the centred fractional derivatives established by Manuel Duarte Ortigueira in 2006 can be used to describe optical solitons. It is demonstrated that a fractional extension of the nonlinear Schrödinger (NLS) equation with Ortigueira's derivatives and soliton solutions may be constructed. This fractional NLS equation also possesses a Lagrangian density and may be derived from a variational principle, as demonstrated. Finally, it is demonstrated that fractional extensions of Noether's theorem may be formulated using either Ortigueira's centred derivatives or Grünwald-derivatives Letnikov's for fractional generalisations of the NLS equation. And we may derive the conserved values associated with the invariances of the action integral under infinitesimal transformations from these extensions of Noether's theorem.

Author(S) Details

J. Fujioka
Instituto de Física, Dpto. de Sistemas Complejos, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000 México D.F., México.

M. Velasco
Colegio de Ciencias y Humanidades, Plantel Oriente, Universidad Nacional Autónoma de México, Ciudad de México, CP 08500, México.

A. Ramírez
Atmospheric Science Graduate Group, University of California, Davis, USA.

A. Espinosa-Cerón
Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México, CP 04510, México.

View Book:- https://stm.bookpi.org/RAMRCS-V9/article/view/6025