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Fr\'olicher-Nijenhuis geometry and integrable matrix PDE systems
- Publication Year :
- 2024
-
Abstract
- Given two tensor fields of type (1,1) on a smooth n-dimensional manifold M, such that all their Fr\"olicher-Nijenhuis brackets vanish, the algebra of differential forms on M becomes a bi-differential graded algebra. As a consequence, there are partial differential equation (PDE) systems associated with it, which arise as the integrability condition of a system of linear equations and possess a binary Darboux transformation to generate exact solutions. We recover chiral models and potential forms of the self-dual Yang-Mills, as well as corresponding generalizations to higher than four dimensions, and obtain new integrable non-autonomous nonlinear matrix PDEs and corresponding systems.<br />Comment: 20 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.01328
- Document Type :
- Working Paper