title: Radiating subdispersive fractional optical solitons.
abstract: It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.
authors.affiliation: Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico, DF 04510, Mexico.
authors.forename: J
authors.initials: J
authors.lastname: Fujioka
authors.affiliation: Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico, DF 04510, Mexico.
authors.forename: A
authors.initials: A
authors.lastname: Espinosa
authors.affiliation: Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico, DF 04510, Mexico.
authors.forename: R F
authors.initials: RF
authors.lastname: Rodríguez
authors.affiliation: Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: B A
authors.initials: BA
authors.lastname: Malomed