Controllable rational solutions in nonlinear optics fibers

Based on Darboux matrix method, a generalized Darboux transformation of a generalized nonlinear Schrödinger equation possessing higher-order terms which refer to a femto second pulse propagation in a nonlinear fiber optic is constructed. This nonlinear Schrödinger equation can model the propagation of soliton in a Heisenberg spin chain. Using the above-generalized Darboux transformation, we calculate the first, two and third-order rogue wave solutions and give general formulae for generating N th-order ones. We discuss the effect of higher-order terms contained in the above equation.