Variable separation and algebro-geometric solutions of the Gerdjikov–Ivanov equation

The Gerdjikov–Ivanov equation is decomposed into two systems of solvable ordinary differential equations. A hyperelliptic Riemann surface and Abel–Jacobi coordinates are introduced to straighten the associated flow, from which the algebro-geometric solutions of the Gerdjikov–Ivanov equation are constructed in terms of the Riemann theta functions.