Projective differential geometry of multidimensional dispersionless integrable hierarchies

Physics and Mathematics of Nonlinear Phenomena 2013

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

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.