Rarefaction waves and dispersive shock waves in fluid dynamics to the higher-order Gerdjikov–Ivanov model

This work develops the Whitham modulation theory to study the Riemann problem of the higher-order Gerdjikov–Ivanov equation. The zero- and one-phase periodic solutions and the corresponding Whitham modulation equations are derived by the finite-gap integration method. The main basic wave structures including rarefaction waves and dispersive shock waves arising from the discontinuous initial value conditions are investigated by distinguishing the distributions of the Riemann invariants.