In the present paper, we construct a particular class of solutions of the sine-Gordon equation, which is the exact analogue of the so-called negatons, a solution class of the Korteweg-de Vries equation discussed by Matveev [17] and Rasinariu et al. [21]. Their characteristic properties are:
Each solution consists of a finite number of clusters. Roughly speaking, in such a cluster solitons are grouped around a center, and the distance between two of them grows logarithmically. The clusters themselves rather behave like solitons. Moving with constant velocity, they collide elastically with the only effect of a phase-shift.
The main contribution of this paper is the proof that all this -including an explicit calculation of the phase-shift- can be expressed by concrete asymptotic formulas, which generalize very naturally the known expressions for solutions.
Our results confirm expectations formulated in the context of the Korteweg-de Vries equation by Matveev (1994) and Rasinariu et al. (1996).
@article{urn:eudml:doc:44401,
title = {Solitons of the sine-Gordon equation coming in clusters.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {15},
year = {2002},
pages = {265-325},
zbl = {1059.35128},
mrnumber = {MR1915225},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44401}
}
Schiebold, Cornelia. Solitons of the sine-Gordon equation coming in clusters.. Revista Matemática de la Universidad Complutense de Madrid, Tome 15 (2002) pp. 265-325. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44401/