Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation

Abstract

In this paper, using the Darboux transformation, we demonstrate the generation of first order breather and higher-order rogue waves from a generalized nonlinear Schrödinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describes the soliton-type nonlinear excitations in classical Heisenberg spin chain. Such solutions have a parameter ${\gamma }_1$, denoting the strength of the higher-order effects. From the numerical plots of the rational solutions, the compression effects of the breather and rogue waves produced by ${\gamma }_1$ are discussed in detail.

20 pages, 7 figures. Several wrong values of $gamm{a}_1$ are corrected

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