Large stable oscillations due to Hopf bifurcations in amplitude dynamics of colliding soliton sequences

Abstract

We demonstrate that the amplitudes of optical solitons in nonlinear multisequence optical waveguide coupler systems with weak linear and cubic gain-loss exhibit large stable oscillations along ultra-long distances. The large stable oscillations are caused by supercritical Hopf bifurcations of the equilibrium states of the Lotka-Volterra (LV) models for dynamics of soliton amplitudes. The predictions of the LV models are confirmed by numerical simulations with the coupled cubic nonlinear Schrödinger (NLS) propagation models with $2\le N\le 4$ pulse sequences. Thus, we provide the first demonstration of intermediate nonlinear amplitude dynamics in multisequence soliton systems, described by the cubic NLS equation. Our findings are also an important step towards realization of spatio-temporal chaos with multiple periodic sequences of colliding NLS solitons.

Longer version with 22 pages and 16 figures

References in corpus (5)

• Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction
• Transmission stability and Raman-induced amplitude dynamics in multichannel soliton-based optical waveguide systems
• Robust transmission stabilization and dynamic switching in broadband hybrid waveguide systems with nonlinear gain and loss
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Cited by in corpus (4)

• Enhancement of transmission quality in soliton-based optical waveguide systems by frequency dependent linear gain-loss and the Raman self-frequency shift
• Stabilizing solitons of the cubic-quintic nonlinear Schrödinger equation by frequency-dependent linear gain-loss and delayed Raman response
• Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg-Landau gain-loss
• Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2