Chirped chiral solitons in nonlinear Schrödinger equation with self-steepening and self-frequency shift

Abstract

We find exact solutions to nonlinear Schrödinger equation in the presence of self-steepening and self-frequency shift. These include periodic solutions and localized solutions of dark-bright type which can be {\emph{chiral}}, and chirality being controlled by sign of self steepening term. A new form of self phase modulation, which can be tuned by higher order nonlinearities as also by the initial conditions, distinct from nonlinear Schrödinger equation, characterizes these solutions. In certain nontrivial parameter domain solutions are found to satisfy {\emph{linear}} Schrödinger equation, indicating possiblity of linear superposition in this nonlinear system. Dark and bright solitons exist in both anomalous and normal dispersion regimes and a duality between dark-bright type of solution and kinematic-higher order chirping is also seen. Localized kink solutions similar to NLSE solitons, but with very different self phase modulation, are identified.

4 pages, ReVTeX format with two figures

References in corpus (1)

• Controlling pulse propagation in optical fibers through nonlinearity and dispersion management

Cited by in corpus (8)

• Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrodinger equation with modulating coefficients
• Cubic-quintic nonlinear Helmholtz equation: Modulational instability, chirped elliptic and solitary waves
• Chirped nonlinear resonant states in femtosecond fiber optics
• Gapped solitons and periodic excitations in strongly coupled BEC
• Coupled Helmholtz Equations : Chirped Solitary Waves
• Some results on topological currents in field theory
• Chirped Elliptic Waves: Coupled Helmholtz Equations
• Phase modulated domain walls and dark solitons for surface gravity waves