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Triangular bright solitons in nonlinear optics and Bose-Einstein condensates.

Liangwei Zeng, Milivoj R Belić, Dumitru Mihalache

|May 9, 2023

Summary

Researchers discovered novel triangular bright solitons, stable under specific conditions in nonlinear optics and Bose-Einstein condensates. These unique solitons exhibit triangular profiles and can transform between forms based on nonlinearity modulation.

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Area of Science:

Nonlinear optics
Quantum physics
Mathematical physics

Background:

Solitons are self-reinforcing solitary waves.
The nonlinear Schrödinger equation (NLSE) models various wave phenomena.
Kerr-like nonlinearity and harmonic potentials are common in physical systems.

Purpose of the Study:

To demonstrate novel triangular bright solitons.
To analyze their stability and propagation characteristics.
To explore their potential in nonlinear optics and Bose-Einstein condensates.

Main Methods:

Theoretical analysis using the NLSE with inhomogeneous nonlinearity and harmonic potential.
Linear stability analysis.
Direct numerical simulations.

Main Results:

Demonstrated stable triangular bright solitons (triangle-up and triangle-down).
Profiles differ significantly from Gaussian or sech solitons.
Modulated propagation depends on nonlinearity strength modulation: gradual changes yield stable solitons, sudden changes cause instability, and periodic changes cause oscillations.
Triangle-up and triangle-down solitons can interconvert.

Conclusions:

Triangular bright solitons are stable and novel solutions to the NLSE.
Their stability and behavior are controllable via nonlinearity modulation.
These findings have implications for optical systems and Bose-Einstein condensates.