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Soliton dynamics in a random Toda chain.
1Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France. garnier@cict.fr
Summary
Solitons in randomly distributed Toda lattices decay differently based on amplitude. A "soliton gas" forms, impacting conservation laws and influencing decay dynamics, especially with long-range correlations.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Statistical mechanics
Background:
- Toda lattices exhibit soliton propagation.
- Random mass distributions introduce complexity to soliton behavior.
- Understanding soliton decay is crucial for nonlinear systems.
Purpose of the Study:
- To investigate soliton dynamics in a Toda lattice with random mass distribution.
- To derive effective equations for soliton amplitude decay considering radiative losses.
- To analyze the formation and impact of soliton gas.
Main Methods:
- Application of the inverse scattering transform.
- Derivation of effective equations for soliton decay.
- Full numerical simulations for validation.
Main Results:
- Soliton energy decays as N(-3/2) for small amplitudes and exp(-N) for large amplitudes.
- Large-amplitude soliton decay rate is independent of incoming energy.
- A soliton gas is generated, influencing conservation equations.
- Long-range correlations lead to conversion into forward-going radiation instead of backscattering.
Conclusions:
- Soliton decay in disordered Toda lattices is amplitude-dependent and influenced by radiative losses.
- The generated soliton gas is a significant factor in understanding system dynamics.
- Correlation length of fluctuations critically affects soliton propagation directionality.