On kinks and other travelling-wave solutions of a modified sine-Gordon equation

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• 作者：Gaetano Fiore ; Gabriele Guerriero ; Alfonso Maio ; Enrico Mazziotti
• 关键词：Josephson junctions ; Dissipative sine ; Gordon equation ; Kinks ; Travelling ; waves solutions
• 刊名：Meccanica
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：50
• 期：8
• 页码：1989-2006
• 全文大小：840 KB
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• 作者单位：Gaetano Fiore (1) (2)
  Gabriele Guerriero (1)
  Alfonso Maio (1)
  Enrico Mazziotti (1)
  
  1. Dipartimento di Matematica e Applicazioni, Università “Federico II- Complesso MSA, Via Cintia, 80126, Naples, Italy
  2. I.N.F.N., Sezione di Napoli, Complesso MSA, V. Cintia, 80126, Naples, Italy
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Civil Engineering
  Automotive and Aerospace Engineering and Traffic
  Mechanical Engineering
  
• 出版者：Springer Netherlands
• ISSN：1572-9648

文摘

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.