Universality of the amplitude shift in fast two-pulse collisions in weakly perturbed linear physical systems
arXiv:1808.04323 · doi:10.1007/s12648-020-01976-0
Abstract
We demonstrate that the amplitude shifts in fast two-pulse collisions in perturbed linear physical systems with weak nonlinear dissipation exhibit universal soliton-like behavior. The behavior is demonstrated for linear optical waveguides with weak cubic loss and for systems described by linear diffusion-advection models with weak quadratic loss. We show that in both systems, the expressions for the collision-induced amplitude shifts due to the nonlinear loss have the same form as the expression obtained for a fast collision between two solitons of the nonlinear Schrödinger equation in the presence of weak cubic loss. Furthermore, we show that the expressions for the amplitude shifts are universal in the sense that they are independent of the exact details of the initial pulse shapes. We demonstrate the universal soliton-like behavior of the collision-induced amplitude shifts by carrying out numerical simulations with the two perturbed coupled linear evolution models with three different initial conditions corresponding to pulses with exponentially decreasing tails, pulses with power-law decreasing tails, and pulses that are initially nonsmooth and that develop significant tails during the collision. In all six cases we observe very good agreement between the analytic predictions for the amplitude shifts and the results of the numerical simulations.
arXiv comment36 pages, 12 figures. arXiv admin note: text overlap with arXiv:1702.05583
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Cited by in corpus (3)
- Fast two-beam collisions in a linear optical medium with weak cubic loss in spatial dimension higher than 1
- Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss
- Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2