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Published on: December 4, 2017
Quasi-one-dimensional solutions and their interaction with two-dimensional dissipative solitons
Orazio Descalzi1, Helmut R Brand
1Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Avenida San Carlos de Apoquindo 2200, Santiago, Chile. odescalzi@miuandes.cl
Summary
Stable quasi-one-dimensional (quasi-1D) solutions exist for the 2D cubic-quintic complex Ginzburg-Landau equation. These solutions form stable compound states and breathing states, with implications for experimental convection studies.
Area of Science:
- Nonlinear dynamics
- Mathematical physics
- Complex systems
Background:
- The cubic-quintic complex Ginzburg-Landau equation models various phenomena, including nonlinear optics and fluid dynamics.
- Understanding the stability and behavior of its solutions is crucial for predicting system dynamics.
Purpose of the Study:
- To investigate the stable existence of quasi-one-dimensional (quasi-1D) solutions.
- To explore the conditions under which these quasi-1D solutions emerge and their stability relative to other solution types.
- To examine the formation of compound states and breathing solutions.
Main Methods:
- Numerical analysis of the two-dimensional cubic-quintic complex Ginzburg-Landau equation.
- Investigation of solution stability across a range of bifurcation parameters.
- Analysis of interactions between quasi-1D solutions and other soliton types.
Main Results:
- Stable quasi-1D solutions were found to exist over a large parameter range.
- These solutions coexist with stable zero solutions, 2D dissipative solitons, and exploding dissipative solitons.
- Stable compound states were formed with stationary and exploding dissipative solitons.
- Stable breathing quasi-1D solutions were identified near the collapse transition.
Conclusions:
- Quasi-1D solutions represent a significant class of stable states in the studied system.
- The findings offer insights into complex pattern formation and stability.
- Analogies are drawn to recent experimental observations in convection systems.
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