2014/06/30 by Jian-Yong Wang, Jianyong Wang, Xiaoyan Tang +5 · 7 citations
Physics and Astronomy · #Advanced Fiber Laser Technologies #Amplitude #Classical mechanics #Cnoidal wave #Core (optical fiber) #Korteweg–de Vries equation #Mathematical physics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Optics #Periodic wave #Physics #Quantum electrodynamics #Quantum mechanics #Soliton #Wave propagation #Wavelength #nlin.SI
paper · pdf · doi:10.1209/0295-5075/108/20005
published in Europhysics Letters (EPL) 108(2), 20005 (Institute of Physics) · 11pages, 4 figures
openalex publication_date 2014/10/01 · arxiv created 2018/05/20 · arxiv updated 2018/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.