Summary
A simple method for studying the Hamiltonian structure of the soliton equations is applied to a new hierarchy of partial differential equations related to a Zhakarov-Shabat-like spectral problem. These soliton equations are shown to be integrable Hamiltonian systems and can be described as motions on a symplectic Kähler manifold.
Riassunto
Si applica un metodo semplice per lo studio della struttura hamiltoniana delle equazioni solitoniche ad una nuova gerarchia di equazioni alle derivate parziali collegate ad un problema spettrale del tipo Zakharov-Shabat. Si mostra che queste equzioni solitoniche sono sistemi hamiltoniani integrabili e possono essere descritte come moti su una varietà simplettica di Kähler.
Резюме
Простой метод для исследования гамильтоновой структуры солитонных уравнений применяется к новой иерархии парциальных дифференциальных уравнений, связанных со спектральной проблемой Захарова-Шабата. Показывается, что эти сплитонные уравнения представляют интегрируемые гамильтоновы системы и могут быть описаны, как движения на симплектическом множестве Келера.
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On leave of absence (up to April 1983) from Computing Centre of Chinese Academy of Sciences, Beijing, China.
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Boiti, M., Tu, G.Z. A simple approach to the Hamiltonian structure of soliton equations. Nuovo Cimento B 75, 145–160 (1983). https://doi.org/10.1007/BF02831169
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DOI: https://doi.org/10.1007/BF02831169