The general coupled Hirota equations: modulational instability and higher-order vector rogue wave and multi-dark...

Area of Science:

• Nonlinear optics
• Fiber optics
• Wave propagation

Background:

• The coupled Hirota equations model ultrashort optical pulse propagation in fibers.
• Understanding vector nonlinear wave phenomena is crucial for optical communications.

Purpose of the Study:

• Investigate modulational instability in focusing, defocusing, and mixed nonlinear systems.
• Derive unified formulas for high-order rational rogue waves (RWs) in vector systems.
• Explore the coexistence of different localized wave structures.

Main Methods:

• Analysis of the general coupled Hirota equations.
• Derivation of formulas for higher-order vector rational RWs and semirational RWs.
• Investigating multi-dark-dark solitons and the coexistence of dark solitons and RWs.

Main Results:

• Unified formulas for high-order rational RWs across different cases.
• Vector rational RWs exhibit richer distribution patterns than scalar models.
• Demonstrated coexistence of vector rational RWs and N-breathers.
• Derived multi-dark-dark solitons and formulas for dark soliton-RW coexistence.

Conclusions:

• The findings enrich the understanding of localized wave excitations in vector nonlinear systems.
• Results provide deeper insights into the applications of nonlinear wave phenomena in fiber optics.