Frölicher–Nijenhuis geometry and integrable matrix PDE systems
Year: 2025
Type: article
Abstract: 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 systems of PDEs 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 equations, as well as corresponding generalizations to higher than four dimensions, and obtain new integrable non-autonomous nonlinear matrix PDEs.
Source: Nonlinearity
Author: Folkert Müller-Hoissen
Institution: University of Göttingen
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4413995149