2021/08/06 by F. Palmero, Faustino Palmero, Mario I. Molina +4
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Breather #Classical mechanics #Instability #Lattice (music) #Linear stability #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Nonlinear system #Operator (biology) #Physics #Quantum mechanics #Schrödinger's cat #math-ph #math.MP #msc:34C15 #nlin.PS
paper · pdf · doi:10.1016/j.physleta.2021.127880
9 pages, 16 figures
arxiv created 2021/08/06 · openalex publication_date 2021/12/01 · arxiv updated 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrodinger equation, where the linear operator of the Schrodinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.