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Time-periodic solitons in a damped-driven nonlinear Schrödinger equation
I V Barashenkov1, E V Zemlyanaya, T C van Heerden
1Department of Mathematics, University of Cape Town, Rondebosch 7701, South Africa. igor.barashenkov@gmail.com
Summary
Time-periodic solitons in a driven damped nonlinear Schrödinger equation exhibit complex behavior. Bifurcation diagrams reveal transitions to temporal chaos, influenced by dissipation and radiation frequencies, linked to homoclinic bifurcation.
Area of Science:
- Nonlinear Dynamics
- Soliton Physics
- Chaos Theory
Background:
- Nonlinear Schrödinger equation (NLSE) models phenomena in optics and Bose-Einstein condensates.
- Parametric driving and damping introduce complex dynamics to NLSE solitons.
- Understanding soliton behavior under these conditions is crucial for controlling nonlinear systems.
Purpose of the Study:
- To investigate time-periodic solitons of the parametrically driven damped NLSE.
- To analyze soliton transformations with varying driver strength.
- To explain attractor chart features using bifurcation diagrams.
Main Methods:
- Solving boundary-value problems on a 2D spatiotemporal domain.
- Analyzing soliton transformations by varying driver strength.
- Constructing bifurcation diagrams to map dynamic regimes.
- Comparing results with direct numerical simulations.
Main Results:
- Bifurcation diagrams explain attractor chart structure.
- Period-doubling transition to temporal chaos observed for low dissipation.
- Absence of period-doubling for higher damping.
- Chaos linked to radiation frequencies and homoclinic bifurcation.
Conclusions:
- Bifurcation analysis provides insight into soliton dynamics.
- Dissipation and radiation frequencies govern the transition to chaos.
- Soliton temporal chaos is related to homoclinic bifurcation.
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