Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrodinger equation with modulating coefficients

Abstract

The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse propagation. We consider optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schrödinger (NLS) equation with space- and time-modulated parameters. A proper transformation is presented to reduce the generalized higher-order NLS equation to the integrable Hirota equation with constant coefficients. This transformation allows us to relate certain class of exact solutions of the generalized higher-order NLS equation to the variety of solutions of the integrable Hirota equation. In particular, we illustrate the approach in terms of two lowest-order rational solutions of the Hirota equation as seeding functions to generate rogue wave solutions localized in time that have complicated evolution in space with or without the differential gain or loss term. We simply analyze the physical mechanisms of the obtained optical rogue waves on the basis of these constraints. Finally, The stability of the obtained rogue-wave solutions is addressed numerically. The obtained rogue wave solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and other fields of nonlinear science as Bose-Einstein condensates and ocean

12 pages, 10 figures

References in corpus (3)

• Localized nonlinear waves in systems with time- and space-modulated nonlinearities
• Exact solutions to three-dimensional generalized nonlinear Schrodinger equations with varying potential and nonlinearities
• Chirped chiral solitons in nonlinear Schrödinger equation with self-steepening and self-frequency shift

Cited by in corpus (11)

• Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrodinger equation
• Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time-symmetric potential
• Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schroedinger equation
• Higher-order rational solitons and rogue-like wave solutions of the (2+1)-dimensional nonlinear fluid mechanics equations
• General high-order rogue waves of the (1+1)-dimensional Yajima-Oikawa system
• Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves
• Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations
• GHW-based Necessary and Sufficient Conditions for Support Constrained Generator Matrices
• Darboux Transformation for the Hirota equation
• Solitonic dynamics and excitations of the nonlinear Schrodinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials
• Method of eigenvalue transformation using dispersion oscillating fiber