会议论文详细信息
Physics and Mathematics of Nonlinear Phenomena 2013 | |
Projective differential geometry of multidimensional dispersionless integrable hierarchies | |
Bogdanov, L.V.^1 ; Konopelchenko, B.G.^2 | |
L.D. Landau ITP RAS, Moscow, Russia^1 | |
Department of Mathematics and Physics ennio de Giorgi, University of Salento and INFN, Lecce, Italy^2 | |
关键词: Closedness; Dispersionless; Integrable equations; Integrable hierarchy; Projective differential geometry; Spectral variables; Vector fields; | |
Others : https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012005/pdf DOI : 10.1088/1742-6596/482/1/012005 |
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来源: IOP | |
【 摘 要 】
We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential m-form Ωmwith the coefficients satisfying the Plucker relations, which is gauge-invariantly closed and its gauge-invariant coordinates (ratios of coefficients) are (locally) holomorphic with respect to one of the variables (the spectral variable). We demonstrate that this form defines a hierarchy of dispersionless integrable equations in terms of commuting vector fields locally holomorphic in the spectral variable. The equations of the hierarchy are given by the gauge-invariant closedness equations.
【 预 览 】
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Projective differential geometry of multidimensional dispersionless integrable hierarchies | 517KB | download |