Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy

Area of Science:

• Nonlinear physics
• Mathematical physics
• Wave phenomena

Background:

• The nonlinear Schrödinger equation (NLSE) is a fundamental model in various fields, including optics and fluid dynamics.
• Rogue waves are extreme, unpredictable wave events that pose significant research interest.
• Previous studies have focused on lower-order NLSE models, leaving higher-order effects less explored.

Purpose of the Study:

• To derive rogue wave solutions for the integrable nonlinear Schrödinger equation hierarchy.
• To incorporate an infinite number of higher-order dispersion and nonlinear terms.
• To provide exact expressions for the properties of these higher-order rogue waves.

Main Methods:

• Analytical derivation of solutions for the NLSE hierarchy.
• Inclusion of higher-order dispersion and nonlinear terms in the model.
• Characterization of rogue wave properties, including velocities, phase, and stretching factors.

Main Results:

• Exact rogue wave solutions for all orders of the NLSE hierarchy were derived.
• Expressions for velocities, phase, and stretching factors of rogue waves were obtained.
• Specific examples of second-order rogue wave solutions, such as rogue wave triplets, were presented.

Conclusions:

• The study successfully extended the analysis of rogue waves to higher-order NLSE models.
• The derived solutions provide a comprehensive framework for understanding complex rogue wave phenomena.
• These findings contribute to the theoretical understanding of extreme wave events in nonlinear systems.