Conditions for soliton trapping in random potentials using Lyapunov exponents of stochastic ODEs. (English) Zbl 1115.82323
Summary: The conditions for trapping of Schrödinger solitons in a random potential are analysed. A stochastic ODE is derived for the position of the soliton centre and the behaviour of its solution is studied for different types of stochasticity. The problem of trapping or propagation of the solitons in the potential is connected with the calculation of the Lyapunov exponents for stochastic ODEs and rigorous criteria for trapping are provided. Possible applications to the problem of strong dispersion management are discussed.
MSC:
| 82B44 | Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
| 34F05 | Ordinary differential equations and systems with randomness |
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