Nanopteron solution of the Korteweg-de Vries equation

The nanopteron, which is a permanent but weakly nonlocal soliton, has been an interesting topic in numerical studies for many decades. However, the analytical solution of such a special soliton is rarely considered. In this letter, we study the explicit nanopteron solution of the Korteweg-de Vries (...

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Bibliographic Details
Published in:Europhysics letters 2014-10, Vol.108 (2), p.20005-p1-20005-p6
Main Authors: Wang, Jianyong, Tang, Xiaoyan, Lou, Senyue, Gao, Xiaonan, Jia, Man
Format: Article
Language:English
Subjects:
02.30.Ik
05.45.Yv
52.35.Mw
Amplitudes
Cnoidal waves
Exact solutions
Korteweg-Devries equation
Mathematical analysis
Mathematical models
Nanostructure
Solitary waves
Solitons
Wave interaction
Wave propagation
Wavelengths
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Summary:The nanopteron, which is a permanent but weakly nonlocal soliton, has been an interesting topic in numerical studies for many decades. However, the analytical solution of such a special soliton is rarely considered. In this letter, we study the explicit nanopteron solution of the Korteweg-de Vries (KdV) equation. Starting from the soliton-cnoidal wave solution of the KdV equation, the nanopteron structure is shown to exist. It is found that for the suitable choice of the wave parameters, the soliton core of the soliton-cnoidal wave trends to be a classical soliton of the KdV equation and the surrounded cnoidal periodic wave appears as small amplitude sinusoidal variations on both sides of the main core. Some interesting features of the wave propagation are revealed. In addition to the elastic interaction, it is surprising that the phase shift of the cnoidal periodic wave after the interaction with the soliton core is always half its wavelength, and this conclusion is universal to soliton-cnoidal wave interactions.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/108/20005