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 - 1990

Fingerprint

sine-Gordon equation
Modulational Instability
Sine-Gordon Equation
Homoclinic Orbit
Orbits
orbits
Geometry
geometry
Orbit
Integrable Equation
Homoclinic
Geometric Structure
Periodic Boundary Conditions
Labeling
Explicit Formula
Torus
marking
catalogs
Boundary conditions
boundary conditions

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Geometry of the modulational instability. III. Homoclinic orbits for the periodic sine-Gordon equation. / Ercolani, N.; Forest, M. G.; McLaughlin, David W.

In: Physica D: Nonlinear Phenomena, Vol. 43, No. 2-3, 1990, p. 349-384.

Research output: Contribution to journalArticle

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