Abstract
The evolution of a propagating kink in a Sine-Gordon lattice is studied asymptotically using an averaged Lagrangian formulation appropriately coupled to the effect of the radiation. We find that unlike the continuum case the interaction with the Goldstone mode is important to explain the acceleration of the kink as it hops along the lattice. We develop a discrete WKB type solution to study the interaction of the kink and the radiation. In particular using this solution we show how to calculate the effect of the Peyrard and Kruskal resonant radiation in the energy loss of the kink. We obtain a set of modulation equation which explains qualitatively the evolution of the kink with remarkable quantitative agreement.
Original language | English |
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Pages (from-to) | 50-65 |
Number of pages | 16 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 237 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2008 |
Externally published | Yes |
Keywords
- Internal modes
- Kink
- Modulation averaged Lagrangian
- Peierls-Nabarro potential
- Radiation damping