Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation

In this paper, using the Darboux transformation, we demonstrate the generation of first order breather and higher-order rogue waves from a generalized nonlinear Schr\"odinger 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.