The multi-positon and breather positon solutions for the higher-order nonlinear Schrödinger equation in optical fibers

Under investigation in this paper is the higher-order nonlinear Schrödinger equation, which can imitate the ultrashort pulses propagation in optical fibers. The modulation instability is analyzed based on the plane-wave solution. With the help of the generalized Darboux transformation, the second-, third- and fourth-order positon solutions are constructed. Furthermore, the second-, third- and fourth-order breather positon solutions are obtained, and the influences of parameters for the characteristics of solutions are analyzed.