Holm Darryl D, Tyranowski Tomasz M
Mathematics Department, Imperial College London, London SW7 2AZ, UK.
Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, 85748 Garching, Germany.
Proc Math Phys Eng Sci. 2018 May;474(2213):20180052. doi: 10.1098/rspa.2018.0052. Epub 2018 May 9.
We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler-Poincaré equations defined on the Virasoro-Bott group, by using the inverse map (also called 'back-to-labels' map). This family contains as special cases the well-known Korteweg-de Vries, Camassa-Holm and Hunter-Saxton soliton equations. In the conclusion section, we sketch opportunities for future work that would apply the new Clebsch momentum map with 2-cocycles derived here to investigate a new type of interplay among nonlinearity, dispersion and noise.
我们通过使用逆映射（也称为“反向标记”映射），推导了一个新的变分原理，从而为定义在维拉索罗 - 博特群上的一族欧拉 - 庞加莱方程得出了一个新的动量映射和一种新的多辛形式。这个族包含著名的科特韦格 - 德弗里斯、卡马萨 - 霍尔姆和亨特 - 萨克斯顿孤子方程作为特殊情况。在结论部分，我们概述了未来工作的机会，即应用在此处推导的带有2 - 上循环的新克莱布施动量映射来研究非线性、色散和噪声之间的新型相互作用。
