no. 21-22
Mathematical Physics
On stable solutions of the finite non-periodic Toda lattice
[Sur les solutions stables du réseau de Toda non périodique fini]

Présenté par : the Editorial Board

Ikeda, Kaoru1
1 The center for Integrative mathematical Science, Hiyoshi Campus, Keio University, Hiyoshi 4-1-1, Kouhoku-ku, Yokohama 223-8521, Japan
Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 985-989.

On étudie les solutions stables du réseau de Toda fini non périodique de type An. On obtient des solutions du réseau de Toda de type An par décomposition de Gauss. Les solutions ainsi obtenues sont instables car la décomposition de Gauss possède des singularités. Les solutions stables obtenues par la méthode de décomposition de Gauss modifiée sont des fonctions entières sur R, elles sont des solutions-solitons.

In this Note we study stable solutions of the finite non-periodic (An-type) Toda lattice. Solutions of the An-type Toda lattice are obtained by Gauss decomposition. Such solutions are unstable because the Gauss decomposition brings singularities. We obtain stable solutions which are entire functions on R as the soliton solutions by modified Gauss decomposition.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.10.020
Ikeda, Kaoru 1

1 The center for Integrative mathematical Science, Hiyoshi Campus, Keio University, Hiyoshi 4-1-1, Kouhoku-ku, Yokohama 223-8521, Japan 
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Ikeda, Kaoru. On stable solutions of the finite non-periodic Toda lattice. Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 985-989. doi : 10.1016/j.crma.2012.10.020. http://www.numdam.org/articles/10.1016/j.crma.2012.10.020/

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