2020/09/01 by N. Karjanto, Karjanto, N. · 3 citations
Engineering · Mathematics · Physics and Astronomy · #35C08 #35Q55 #35Q60 #37K40 #76B15 #Advanced Mathematical Physics Problems #Bifurcation #Breather #Classical mechanics #Engineering #Envelope (radar) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Homoclinic orbit #Limiting #Mathematical physics #Modulational instability #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Nonlinear system #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS) #Physics #Quantum electrodynamics #Quantum mechanics #Rogue wave #Soliton #Telecommunications #Waveform #msc:35C08 #msc:35Q55 #msc:35Q60 #msc:37K40 #msc:76B15 #nlin.PS #physics.flu-dyn #physics.optics
paper · pdf · doi:10.48550/arxiv.2009.00269
published in arXiv (Cornell University) (Cornell University) · 29 pages, 8 figures, 159 references
arxiv created 2020/09/01 · openalex publication_date 2020/09/01 · arxiv updated 2020/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schrödinger (NLS) equation. These breathers belong to the families of solitons on a non-vanishing and constant background, where the continuous-wave envelope serves as a pedestal. The rational Peregrine soliton acts as a limiting behavior of the other two breather solitons, i.e., the Kuznetsov-Ma breather and Akhmediev soliton. Albeit with a phase shift, the latter becomes a nonlinear extension of the homoclinic orbit waveform corresponding to an unstable mode in the modulational instability phenomenon. All breathers are prototypes for rogue waves in nonlinear and dispersive media. We present a rigorous proof using the ε-δ argument and show the corresponding visualization for this limiting behavior.