Analytical solutions of the Gerdjikov–Ivanov equation by using exp(−φ(ξ))-expansion method

Abstract

The Gerdjikov–Ivanov equation which appears in quanta field theory, nonlinear optics, weak nonlinear dispersive water wave, etc., is discussed. We study a new direct approach namely exp(−φ(ξ))-expansion method to seek exact solutions of Gerdjikov–Ivanov equation which include variety of models. These exact solutions include the hyperbolic, trigonometric, rational and exponential functions with some arbitrary parameters. It is shown that the method is quite efficient and useful to obtain exact solutions of different types of nonlinear differential equations.