Nonparaxial rogue waves in optical Kerr media

Abstract

We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.

Dipole and quadrupole nonparaxial solitary waves

“…Quasi soliton behavior of the exact as well as approximate solutions to the scalar and vector nonparaxial evolution equations developed for describing propagation in two dimensions, are shown in [18]. Vortex solitons in two dimensions [19], rogue waves [21], and numerical solutions to the nonparaxial nonlinear Schödinger equation are obtained in [20]. The study of nonparaxiality in PT -symmetric optical context is found in [22].…”

Darboux Transformation for the 3-Dimension Nonlinear Schrodinger Equation

“…Focused on a variable-coefficient coherently coupled NLS system, and when the inhomogeneities of fibers and nonuniformities of boundaries are considered, the coupled NLS systems with the variable coefficients are better than that by constructing the constant-counterparts to describe the corresponding physical phenomena [14], [15]. Because the Darboux transformation can be adopted to choose the specific set of parameters and free functions, the first-and second-order rational solutions of the nonparaxial NLS equation were presented in [14]. Actually, the peak height of a high-order breather is just a sum of peak heights of first-order breathers plus that of the background.…”