Título inglés | Solitons of the sine-Gordon equation coming in clusters. |
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Título español | Solitones de la ecuación seno-Gordon en forma de agrupamientos. |
Autor/es | Schiebold, Cornelia |
Organización | Fak. Math. Informat. Univ. Jena, Jena, Alemania |
Revista | 1139-1138 |
Publicación | 2002, 15 (1): 265-325, 27 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | 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). |
Clasificación UNESCO | 120220 |
Palabras clave español | Ecuaciones diferenciales en derivadas parciales ; Solitones ; Ecuaciones de evolución no lineales |
Código MathReviews | MR1915225 |
Código Z-Math | Zbl 1059.35128 |
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