Vector bright solitons associated with positive coherent coupling via Darboux transformation

Area of Science:

• Nonlinear optics
• Waveguide optics
• Mathematical physics

Background:

• Coherent coupling and orthogonally polarized waveguide modes are crucial in nonlinear media.
• Vector bright solitons exhibit complex dynamics influenced by nonlinear effects.
• Integrability of coupled nonlinear systems is key to understanding soliton behavior.

Purpose of the Study:

• To analyze vector bright solitons in Kerr media with positive coherent coupling.
• To derive and present N-soliton solutions using Darboux transformations.
• To investigate soliton collision mechanisms and their properties.

Main Methods:

• Studying coherently coupled and orthogonally polarized waveguide modes.
• Computing conserved quantities and conservation laws.
• Applying the iterative algorithm of Darboux transformation.
• Analyzing soliton collisions with varying parameters.

Main Results:

• Formulas for one-, two-, and N-soliton solutions were derived.
• The integrability of the two-coupled nonlinear Schrödinger system was confirmed via Lax pair.
• Elastic collision mechanisms of vector bright solitons with different profiles were demonstrated.
• The influence of group velocity dispersion, self-phase modulation, cross-phase modulation, and coherent coupling on collisions was shown.

Conclusions:

• The study successfully describes vector bright solitons in coherently coupled Kerr waveguide systems.
• The derived N-soliton solutions and demonstrated elastic collisions provide insights into nonlinear light propagation.
• The integrability of the system suggests potential for further analytical and numerical investigations.