In this Note we study stable solutions of the finite non-periodic (-type) Toda lattice. Solutions of the -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 as the soliton solutions by modified Gauss decomposition.
On étudie les solutions stables du réseau de Toda fini non périodique de type . On obtient des solutions du réseau de Toda de type 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 , elles sont des solutions-solitons.
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Kaoru Ikeda 1
@article{CRMATH_2012__350_21-22_985_0, author = {Kaoru Ikeda}, title = {On stable solutions of the finite non-periodic {Toda} lattice}, journal = {Comptes Rendus. Math\'ematique}, pages = {985--989}, publisher = {Elsevier}, volume = {350}, number = {21-22}, year = {2012}, doi = {10.1016/j.crma.2012.10.020}, language = {en}, }
Kaoru Ikeda. On stable solutions of the finite non-periodic Toda lattice. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 985-989. doi : 10.1016/j.crma.2012.10.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.020/
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