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Coalescence cascade of dissipative solitons in parametrically driven systems
M G Clerc1, S Coulibaly, L Gordillo
1Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
Summary
Parametrically driven systems form dissipative solitons that interact and coalesce. This multisoliton coarsening follows a self-similar law, observed across models and experiments.
Area of Science:
- Nonlinear dynamics
- Soliton physics
- Complex systems
Background:
- Parametrically driven spatially extended systems can exhibit uniform oscillations.
- These oscillations are often modulationally unstable, leading to complex emergent behaviors.
- Dissipative solitons are localized structures that can form and interact in such systems.
Purpose of the Study:
- To investigate the formation and evolution of dissipative solitons in parametrically driven systems.
- To analytically derive and characterize the multisoliton coarsening process.
- To validate the findings across different theoretical models and experimental observations.
Main Methods:
- Analytical derivation of the multisoliton coarsening law, starting from the soliton pair interaction law.
- Numerical simulations using models like the parametrically driven damped nonlinear Schrödinger equation, a driven chain of pendula, and a forced magnetic wire.
- Experimental observation in a vertically oscillated quasi-one-dimensional layer of Newtonian fluid.
Main Results:
- Parametrically driven systems generate a gas of dissipative solitons.
- These solitons undergo a cascade of coalescence processes (coarsening).
- The average soliton separation distance follows a temporal self-similar law during coarsening, consistent across models and experiments.
Conclusions:
- The multisoliton coarsening process in parametrically driven systems is analytically tractable and follows a universal self-similar law.
- The observed phenomena are robust, appearing in diverse physical systems.
- This work provides a unified understanding of soliton dynamics in driven nonlinear systems.
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