Bifurcations and Exact Solutions of the Gerdjikov-Ivanov Equation

Abstract

For the Gerdjikov-Ivanov equation, by using the method of dynamical system, this paper investigates the exact explicit solutions with the form $q(x, t) = \phi(\xi) {\rm exp} [i(\kappa x-\omega t +\theta(\xi)],\xi= x-ct.$ In the given parameter regions, more than 14 explicit exact parametric representations are presented.