# Solitons of the sine-Gordon equation coming in clusters.

Revista Matemática Complutense (2002)

- Volume: 15, Issue: 1, page 265-325
- ISSN: 1139-1138

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topSchiebold, Cornelia. "Solitons of the sine-Gordon equation coming in clusters.." Revista Matemática Complutense 15.1 (2002): 265-325. <http://eudml.org/doc/44401>.

@article{Schiebold2002,

abstract = {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).},

author = {Schiebold, Cornelia},

journal = {Revista Matemática Complutense},

keywords = {Ecuaciones diferenciales en derivadas parciales; Solitones; Ecuaciones de evolución no lineales; exact solutions; negatons; cluster; phase-shift; asymptotic formulas},

language = {eng},

number = {1},

pages = {265-325},

title = {Solitons of the sine-Gordon equation coming in clusters.},

url = {http://eudml.org/doc/44401},

volume = {15},

year = {2002},

}

TY - JOUR

AU - Schiebold, Cornelia

TI - Solitons of the sine-Gordon equation coming in clusters.

JO - Revista Matemática Complutense

PY - 2002

VL - 15

IS - 1

SP - 265

EP - 325

AB - 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).

LA - eng

KW - Ecuaciones diferenciales en derivadas parciales; Solitones; Ecuaciones de evolución no lineales; exact solutions; negatons; cluster; phase-shift; asymptotic formulas

UR - http://eudml.org/doc/44401

ER -

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