Robert ConteENS Paris-Saclay, France and U of Hong Kong, A. Michel GrundlandUQTR, Canada
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引用次数: 0
摘要
我们导出了由Konopelchenko和Rogers引入的两个耦合正弦- gordon方程组对常微分方程的所有化简。所有这些约简都是对Chazy发现的一个“对其优雅感到好奇”的方程的主约简的简并，这是painleve最一般的第六方程的代数变换。-- -- Nous 'etablissons吹捧les ' educations du system ' eme de deux 'equations ' couples ' es de sin - gordon介绍parkonopelchenko和Rogers ' a des 'equations diff ' entientielles ordinaires。Ces r \ '排出的书桌\ '如\ ' en \ '一个r erescences \“马排出{\ ^ \我}tresse \ '一个\“equationjug \”ee par Chazy“curieuse en雷森(儿子)\ ' el \ ' egance”,变换\ ' eealg \ ' ebrique de la泗溪\“高速\”方程de Painlev \“e la + g \ ' \ ' erale。
Réductions d'un système bidimensionnel de sine-Gordon à la sixième équation de Painlevé
We derive all the reductions of the system of two coupled sine-Gordon
equations introduced by Konopelchenko and Rogers to ordinary differential
equations. All these reductions are degeneracies of a master reduction to an
equation found by Chazy "curious for its elegance", an algebraic transform of
the most general sixth equation of Painlev\'e. -- -- Nous \'etablissons toutes les r\'eductions du syst\`eme de deux \'equations
coupl\'ees de sine-Gordon introduit par Konopelchenko et Rogers \`a des
\'equations diff\'erentielles ordinaires. Ces r\'eductions sont toutes des
d\'eg\'en\'erescences d'une r\'eduction ma{\^\i}tresse \`a une \'equation
jug\'ee par Chazy "curieuse en raison de [son] \'el\'egance", transform\'ee
alg\'ebrique de la sixi\`eme \'equation de Painlev\'e la plus g\'en\'erale.
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