Indexed on: 30 Nov '16Published on: 30 Nov '16Published in: Advances in difference equations
We consider the integrable generalization of the nonlinear Schrödinger equation that arises as a model for nonlinear pulse propagation in monomode optical fibers. The existent conditions for its modulational instability to form the rogue waves is given from its plane-wave solutions. We propose a generalized \((n,N-n)\)-fold Darboux transformation for this system by using the Nth-order Darboux matrix, Taylor expansion, and a limit procedure. As an application, we use the generalized perturbation \((1,N-1)\)-fold Darboux transformation to generate higher-order rogue wave solutions of this system. The dynamics behavior of the first-, second-, and third-order rouge wave solutions are shown graphically. These results may be useful for understanding some physical phenomena in optical fibers.