Emission of radiation by a KdV soliton in a periodic relief

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Abstract

Emission of radiation by a soliton in a spatially periodic relief, which moves with a velocity close to that of the soliton, is analyzed by means of perturbation theory. The moving relief may be generated by a periodic chain of dipoles (modelling small bodies moving in shallow water), or by a cnoidal wave in another mode, coupled to the KdV equation. The main result is that, unlike the typical situation in other nonlinear systems, the relief does not capture the soliton. On the contrary, under the action of the radiative losses, a soliton which was moving slower than the relief is further decelerated, while one which was faster is accelerated, so that the relief induces a repelling separatrix in the velocity space. This "anomalous" behaviour is stipulated by the lack of positive definiteness of energy in the KdV system.

Original languageEnglish
Pages (from-to)373-377
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume172
Issue number5
DOIs
StatePublished - 11 Jan 1993
Externally publishedYes

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