Nanopteron solution of the Korteweg-de Vries equation
| Autor: | Xiao-Nan Gao, Jian-Yong Wang, Xiao-yan Tang, Man Jia, S. Y. Lou |
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| Rok vydání: | 2014 |
| Předmět: |
Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems Structure (category theory) General Physics and Astronomy FOS: Physical sciences Small amplitude Core (optical fiber) Wavelength Classical mechanics Nonlinear Sciences::Exactly Solvable and Integrable Systems Periodic wave Soliton Exactly Solvable and Integrable Systems (nlin.SI) Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons |
| DOI: | 10.48550/arxiv.1406.6629 |
| Popis: | The nanopteron, which is a permanent but weakly nonlocal soliton, has been an interesting topic in numerical study for many decades. However, 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 of its wavelength, and this conclusion is universal to soliton-cnoidal wave interactions. Comment: 11pages, 4 figures |
| Databáze: | OpenAIRE |
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