Radiation dynamics in fast soliton collisions in the presence of cubic loss

Abstract

We study the dynamics of emission of radiation (small-amplitude waves) in fast collisions between two solitons of the nonlinear Schrödinger (NLS) equation in the presence of weak cubic loss. We calculate the radiation dynamics by a perturbation technique with two small parameters: the cubic loss coefficient ${\epsilon }_3$ and the reciprocal of the group velocity difference $1/\beta$. The agreement between the perturbation theory predictions and the results of numerical simulations with the full coupled-NLS propagation model is very good for large $\beta$ values, and is good for intermediate $\beta$ values. Additional numerical simulations with four simplified NLS models show that the differences between perturbation theory and simulations for intermediate $\beta$ values are due to the effects of Kerr nonlinearity on interpulse interaction in the collision. Thus, our study demonstrates that the perturbation technique that was originally developed to study radiation dynamics in fast soliton collisions in the presence of conservative perturbations can also be employed for soliton collisions in the presence of dissipative perturbations.

arXiv comment50 pages, 48 figures

References in corpus (8)

• Theory of Bose-Einstein condensation in trapped gases
• Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
• Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems
• Multiple Breakup of Higher-Order Spatial Solitons
• Diverging probability density functions for flat-top solitary waves
• Transmission stability and Raman-induced amplitude dynamics in multichannel soliton-based optical waveguide systems
• Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems
• Stabilizing soliton-based multichannel transmission with frequency dependent linear gain-loss

Cited by in corpus (7)

• Analysis of a Crank-Nicolson finite difference scheme for (2+1)D perturbed nonlinear Schrödinger equations with saturable nonlinearity
• Stabilizing solitons of the cubic-quintic nonlinear Schrödinger equation by frequency-dependent linear gain-loss and delayed Raman response
• Collision-induced amplitude dynamics of fast 2D solitons in saturable nonlinear media with weak nonlinear loss
• Fast two-beam collisions in a linear optical medium with weak cubic loss in spatial dimension higher than 1
• Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg-Landau gain-loss
• Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss
• Stabilizing optical solitons by frequency-dependent linear gain-loss and the collisional Raman frequency shift