Geometry of the modulational instability. III. Homoclinic orbits for the periodic sine-Gordon equation

N. Ercolani, M. G. Forest, David W. McLaughlin

Research output: Contribution to journalArticle

Abstract

In this paper the homoclinic geometric structure of the integrable sine-Gordon equation under periodic boundary conditions is developed. Specifically, focus is given to orbits homoclinic to N-tori. Simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given. A labeling is provided which identifies and catalogues all such orbits. These orbits are related in a one-to-one manner to linearized instabilities. Explicit formulas for all homoclinic orbits are given in terms of Bäcklund transformations.

Original languageEnglish (US)
Pages (from-to)349-384
Number of pages36
JournalPhysica D: Nonlinear Phenomena
Volume43
Issue number2-3
DOIs
StatePublished - Jul 1990

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Geometry of the modulational instability. III. Homoclinic orbits for the periodic sine-Gordon equation'. Together they form a unique fingerprint.

  • Cite this