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Radiating subdispersive fractional optical solitons
J Fujioka1, A Espinosa1, R F Rodríguez1
1Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico, DF 04510, Mexico.
Chaos (Woodbury, N.Y.)
|October 3, 2014
Summary
Researchers explored fractional extensions of the nonlinear Schrödinger (NLS) equation. A new fractional NLS equation with a temporal fractional derivative (TFD) of order α < 2 describes radiating solitons and conserves key physical quantities.
Area of Science:
- Nonlinear Physics
- Soliton Dynamics
- Fractional Calculus
Background:
- Previous work established fractional nonlinear Schrödinger (NLS) equations with temporal fractional derivatives (TFDs) of order α > 2 for solitary wave propagation.
- The behavior of solitons under different fractional derivative orders was not fully understood.
Purpose of the Study:
- To investigate a novel fractional extension of the NLS equation involving a TFD of order α < 2.
- To analyze the propagation characteristics of solitons described by this new fractional NLS equation.
- To explore the underlying physical mechanisms and conservation laws associated with this model.
Main Methods:
- Development of a fractional nonlinear Schrödinger (NLS) equation with a temporal fractional derivative (TFD) of order α < 2.
- Analysis of radiating soliton propagation within this fractional NLS framework.
- Investigation of resonances between pulses and linear modes to explain radiation emission.
- Derivation of the fractional NLS equation from a Lagrangian density.
- Application of a fractional Noether's theorem to identify conserved quantities.
Main Results:
- The new fractional NLS equation with α < 2 accurately describes the propagation of radiating solitons.
- Radiation emission is attributed to frequency resonances between the solitons and the system's linear modes.
- The fractional NLS equation is derivable from a Lagrangian.
- Conservation of Hamiltonian, momentum, and energy is predicted by the fractional Noether's theorem.
Conclusions:
- A new fractional nonlinear Schrödinger (NLS) equation with a temporal fractional derivative (TFD) of order α < 2 governs radiating soliton propagation.
- Resonance phenomena explain the radiation emitted by these solitons.
- Fundamental conservation laws (Hamiltonian, momentum, energy) are preserved in this fractional system, as indicated by the fractional Noether's theorem.
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