KdV-soliton dynamics in a random field
| Autor: | L. V. Sergeeva, Efim Pelinovsky |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Quantum optics
Physics Nuclear and High Energy Physics Random field Field (physics) Mathematical analysis Astronomy and Astrophysics Statistical and Nonlinear Physics Limiting case (mathematics) Electronic Optical and Magnetic Materials Amplitude Quantum mechanics Soliton Electrical and Electronic Engineering Falling (sensation) Korteweg–de Vries equation |
| Zdroj: | Radiophysics and Quantum Electronics. 49:540-546 |
| ISSN: | 1573-9120 0033-8443 |
| DOI: | 10.1007/s11141-006-0087-0 |
| Popis: | We consider the interaction between soliton and a spatially uniform external random field within the framework of the forced Korteweg-de Vries equation. In the general case, the averaged soliton field is transformed to a Gaussian pulse whose amplitude falls off with time as t−α, while its width increases as tα, where the parameter α is characterized by the statistical properties of the external force. We obtain an analytical solution for α = 2, which corresponds to the limiting case of an infinitely long correlation time (τ0 → ∞). The obtained solution is compared with the well-known Wadati solution for the case of a delta-correlated external force (τ0 → 0) where the soliton is transformed to a Gaussian pulse with amplitude falling off at a lower rate α = 3/2. The numerical solutions of the forced Korteweg-de Vries equation, which demonstrate an increase in the parameter α from 3/2 to 2 with increasing correlation time, are given for the intermediate case corresponding to 0 < τ0 < ∞. It is shown that the amplitude of the averaged soliton in a periodic random field falls off as t−1 for the long times t. In this case, two pulses propagating in different directions are formed. |
| Databáze: | OpenAIRE |
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