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

This work develops the Whitham theory to study the Riemann problem of the Gerdjikov-Ivanov equation that describes the photon fluid with quintic nonlinearity. The one-phase periodic solution of the Gerdjikov-Ivanov equation and the corresponding Whitham equation are derived by the finite gap integration method. Subsequently, the main basic wave structures arising from the discontinuous initial-value conditions are found by distinguishing the distributions of the Riemann invariants. Some exotic optical undular bores are observed by classifying the solutions of the Riemann problem of the Gerdjikov-Ivanov equation. It is observed that the analytical results from Whitham theory are in excellent agreement with the numerical solutions.