Optical undular bores in Riemann problem of photon fluid with quintic nonlinearity

Area of Science:

• Nonlinear Physics
• Optics
• Fluid Dynamics

Background:

• The Gerdjikov-Ivanov equation models nonlinear phenomena in optics, specifically photon fluid dynamics.
• Understanding wave structures and solutions is crucial for advancements in optical technologies.

Purpose of the Study:

• To apply Whitham theory to the Riemann problem of the Gerdjikov-Ivanov equation.
• To derive and analyze one-phase periodic solutions and their associated Whitham equations.
• To investigate exotic optical undular bores arising from discontinuous initial conditions.

Main Methods:

• Finite gap integration method for deriving solutions.
• Whitham theory for analyzing wave phenomena.
• Classification of Riemann problem solutions to identify wave structures.

Main Results:

• Derivation of one-phase periodic solutions for the Gerdjikov-Ivanov and Whitham equations.
• Identification of basic wave structures based on Riemann invariant distributions.
• Observation of exotic optical undular bores.
• Excellent agreement between Whitham theory predictions and numerical solutions.

Conclusions:

• Whitham theory provides an effective analytical framework for studying the Gerdjikov-Ivanov equation.
• The study reveals novel optical undular bore phenomena in photon fluid dynamics.
• The findings validate the accuracy of Whitham theory against numerical simulations.