Fr\"olicher-Nijenhuis geometry and integrable matrix PDE systems

Folkert Müller-Hoissen

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arXiv · 2409.01328

Fr\"olicher-Nijenhuis geometry and integrable matrix PDE systems

Folkert Müller-Hoissen

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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.

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Folkert Müller-Hoissen. 2024-09-02. Fr\"olicher-Nijenhuis geometry and integrable matrix PDE systems. https://arxiv.org/abs/2409.01328

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