Abstract
We consider the integrable generalization of the nonlinear Schrodinger 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.
Highlights
Rogue waves (RWs) have attracted more and more theoretical and experimental attention [ ]
The rogue waves (RWs) were first observed in deep oceans, and later these studies gradually extended to other fields, such as fiber optics, Bose-Einstein condensates, and capillary waves [ – ]
RWs are taken as a new type of explicit rational solutions of nonlinear wave equations
Summary
Rogue waves (RWs) have attracted more and more theoretical and experimental attention [ ]. RWs are taken as a new type of explicit rational solutions of nonlinear wave equations. Many nonlinear Schrödinger-type equations have been reported to have rogue wave solutions [ – ]. In [ ], multirogue wave solutions of a Schrödinger equation with higher-order terms employing the generalized DT and some related properties of the nonautonomous rogue waves are investigated analytically. Based on the similarity transformation, several families of nonautonomous wave solutions have been studied for the generalized coupled cubic-quintic nonlinear Schrödinger equation with group-velocity dispersion, fiber gain-or-loss, and nonlinearity coefficient functions, which describes the evolution of a slowly varying wave packet envelope in the inhomogeneous optical fiber [ ]. The N th-order rogue wave solutions have been obtained for a
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