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 language | English (US) |
|---|---|
| Pages (from-to) | 349-384 |
| Number of pages | 36 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 43 |
| Issue number | 2-3 |
| DOIs | |
| State | Published - 1990 |
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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 journal › Article
}
TY - JOUR
T1 - Geometry of the modulational instability. III. Homoclinic orbits for the periodic sine-Gordon equation
AU - Ercolani, N.
AU - Forest, M. G.
AU - McLaughlin, David W.
PY - 1990
Y1 - 1990
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=0001522381&partnerID=8YFLogxK
U2 - 10.1016/0167-2789(90)90142-C
DO - 10.1016/0167-2789(90)90142-C
M3 - Article
VL - 43
SP - 349
EP - 384
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 2-3
ER -