标题：Modulational instability and higher-order rogue wave solutions for an integrable generalization of the nonlinear Schrödinger equation in monomode optical fibers
摘要：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 ) $(n,N-n)$ -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 ) $(1,N-1)$ -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.
