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/