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INICIO | 19 de abril de 2024
  

Solitons of the sine-Gordon equation coming in clusters.

Título inglés Solitons of the sine-Gordon equation coming in clusters.
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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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
rmm()icmat.es