Optical solitons and other solutions to Kaup–Newell equation with Jacobi elliptic function expansion method

In this paper, we studied Kaup–Newell (KN) equation in coupled vector form without four-wave mixing terms in birefringent fibers. We employed Jacobi elliptic function expansion method in order to demonstrate sub-pico-second optical soliton solutions. Beside bright and dark solitons, Jacobi elliptic function solutions and hyperbolic solutions are obtained. Moreover, the graphs for some solution are presented. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.