2005/12/31 by Gaetano Fiore, Gabriele Guerriero, Alfonso Maio +1 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Bounded function #Constant (computer programming) #Dissipative system #Geometry #Josephson effect #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Perturbation (astronomy) #Physics #Quantum mechanics #Real line #Sine #Soliton #Superconductivity #Term (time) #Traveling wave #Type (biology) #math-ph #math.MP #msc:35Q51 #msc:37K45 #sine-Gordon equation
paper · pdf · doi:10.1007/s11012-015-0143-y
published in Meccanica 50(8), 1989-2006 (Springer Science+Business Media) · Latex file, 25 pages, 4 figures. Final version to appear in "Meccanica"
openalex publication_date 2015/03/20 · arxiv created 2015/07/07 · arxiv updated 2016/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. On the real line candidate orbitally stable solutions with bounded energy density are either the constant one, or of kink (i.e. soliton) type, or of array-of-kinks type, or of "half-array-of-kinks" type. While the first three have unperturbed analogs, the last type is essentially new. We also propose a convergent method of successive approximations of the (anti)kink solution based on a careful application of the fixed point theorem.