双分量Camassa-Holm系统完全可积性的拉格朗日观点

Journal of Integrable Systems Pub Date : 2016-05-19 DOI:10.1093/integr/xyx002

Jonathan Eckhardt, Katrin Grunert

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引用次数: 7

摘要

我们展示了双分量Camassa-Holm系统从欧拉坐标到拉格朗日坐标的变化如何可以根据潜在等谱问题的某些重新参数化来理解。各自的坐标对应于相关一阶系统的不同归一化。特别地，我们将看到在拉格朗日变量下的双分量Camassa-Holm系统也是完全可积的。

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A Lagrangian View on Complete Integrability of the Two-Component Camassa–Holm System

We show how the change from Eulerian to Lagrangian coordinates for the two-component Camassa–Holm system can be understood in terms of certain reparametrizations of the underlying isospectral problem. The respective coordinates correspond to different normalizations of an associated first order system. In particular, we will see that the two-component Camassa–Holm system in Lagrangian variables is completely integrable as well.

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Journal of Integrable Systems

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