2024/09/02 by Folkert Müller-Hoissen, Müller-Hoissen, Folkert
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2409.01328
Given two tensor fields of type (1,1) on a smooth n-dimensional manifold M, such that all their Frölicher-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.