Painlevé analysis and exact solution to the traveling wave reduction of nonlinear differential equations for describing pulse in optical fiber

Abstract

Two high-order nonlinear partial differential equations are considered. They are used for describing propagation pulses in optical fibers. The Painlevé analysis for traveling wave reduction of the equations is completed. As a result of Painlevé test the condition on some parameters of the models are obtained. For constructing the exact solution, simplest equations method is used. Periodic and solitary wave solutions are found.