Projective differential geometry of multidimensional dispersionless integrable hierarchies
Abstract
We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential m-form Ωm with the coefficients satisfying the Plücker 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.
- Publication:
-
Journal of Physics Conference Series
- Pub Date:
- March 2014
- DOI:
- 10.1088/1742-6596/482/1/012005
- arXiv:
- arXiv:1310.0203
- Bibcode:
- 2014JPhCS.482a2005B
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- General Relativity and Quantum Cosmology;
- Mathematical Physics;
- Mathematics - Differential Geometry
- E-Print:
- 10 pages, the text of the talk at PMNP2013 (Gallipoli, Italy, 22-29 June 2013)