2012/10/31 by Christopher K. R. T. Jones, Robert Marangell, Peter D. Miller +2 · 37 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Classical mechanics #Computer science #Exponential function #Geometry #Gravitational wave #Instability #Mathematical analysis #Mathematics #Mechanics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Sine #Sine wave #Stability (learning theory) #Superluminal motion #Traveling wave #math.AP #math.CA #msc:34D20 #msc:34D23 #msc:35P05 #msc:37C75 #msc:47A75 #msc:47B38
paper · pdf · doi:10.1016/j.physd.2013.02.003
published in Physica D Nonlinear Phenomena 251, 63-74 (Elsevier BV) · 22 pages, 6 figures
arxiv created 2013/01/31 · openalex publication_date 2013/02/10 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the spectral stability properties of periodic traveling waves in the sine-Gordon equation, including waves of both subluminal and superluminal propagation velocities as well as waves of both librational and rotational types. We prove that only subluminal rotational waves are spectrally stable and establish exponential instability in the other three cases. Our proof corrects a frequently cited one given by Scott.