Nonlocal solitons in fractional dimensions

Area of Science:

• Nonlinear optics
• Soliton physics
• Fractional calculus

Background:

• Nonlinear Schrödinger equation governs light propagation.
• Fractional diffraction and nonlocal Kerr nonlinearity present unique challenges.
• Stability of multipole-mode solitons is crucial for applications.

Purpose of the Study:

• Investigate the existence and stability of multipole-mode solitons.
• Explore the role of fractional diffraction and nonlocal nonlinearity.
• Establish conditions for stable soliton propagation in novel configurations.

Main Methods:

• Numerical simulations based on the nonlinear Schrödinger equation.
• Analysis of propagation constants and stability criteria.
• Comparison with conventional nonlocal systems.

Main Results:

• Existence and stable propagation of multipole-mode solitons confirmed.
• Stable propagation achieved for solitons with arbitrary peak numbers.
• Fractional systems allow stable higher-order solitons, unlike conventional systems.

Conclusions:

• Nonlocal solitons can propagate stably in fractional systems.
• Fractional diffraction enables stable higher-order multipole-mode solitons.
• This work presents the first example of nonlocal solitons in fractional settings.