Interaction of dissipative solitons stabilized by nonlinear gradient terms

Area of Science:

• Nonlinear physics
• Optical solitons

Background:

• Dissipative solitons are crucial in nonlinear systems.
• Nonlinear gradient terms stabilize solitons in the cubic complex Ginzburg-Landau equation.

Purpose of the Study:

• Investigate soliton interactions stabilized by nonlinear gradient terms.
• Analyze the impact of the Raman effect-associated nonlinear gradient term on soliton collisions.

Main Methods:

• Numerical simulations of the cubic complex Ginzburg-Landau equation.
• Analysis of soliton collision dynamics under varying nonlinear gradient term magnitudes.

Main Results:

• Identified up to seven distinct collision outcomes: bound states (stationary, oscillatory, meandering, large-amplitude), partial/complete annihilation, and interpenetration.
• Meandering and large-amplitude oscillatory bound states are specific to coupled cubic complex Ginzburg-Landau equations.
• Discovered a linear relationship between oscillation amplitude and period for large-amplitude oscillations.

Conclusions:

• The Raman effect's nonlinear gradient term significantly influences soliton interaction outcomes.
• Specific bound states are unique to certain complex Ginzburg-Landau equation formulations.
• The study provides insights into soliton dynamics and stability in nonlinear optical systems.