# 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:

- Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico, DF 04510 (Mexico)
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

- Publication Date:

- OSTI Identifier:
- 22351018

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EMISSION; EQUATIONS; HAMILTONIANS; LAGRANGIAN FUNCTION; NONLINEAR PROBLEMS; PULSES; SOLITONS

### Citation Formats

```
Fujioka, J., E-mail: fujioka@fisica.unam.mx, Espinosa, A., Rodríguez, R. F., and Malomed, B. A.
```*Radiating subdispersive fractional optical solitons*. United States: N. p., 2014.
Web. doi:10.1063/1.4892616.

```
Fujioka, J., E-mail: fujioka@fisica.unam.mx, Espinosa, A., Rodríguez, R. F., & Malomed, B. A.
```*Radiating subdispersive fractional optical solitons*. United States. doi:10.1063/1.4892616.

```
Fujioka, J., E-mail: fujioka@fisica.unam.mx, Espinosa, A., Rodríguez, R. F., and Malomed, B. A. Mon .
"Radiating subdispersive fractional optical solitons". United States.
doi:10.1063/1.4892616.
```

```
@article{osti_22351018,
```

title = {Radiating subdispersive fractional optical solitons},

author = {Fujioka, J., E-mail: fujioka@fisica.unam.mx and Espinosa, A. and Rodríguez, R. F. and Malomed, B. A.},

abstractNote = {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.},

doi = {10.1063/1.4892616},

journal = {Chaos (Woodbury, N. Y.)},

number = 3,

volume = 24,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}