Double-pole and V-shape resonance soliton solutions are constructed for the U(2) Yang equation on ultrahyperbolic space, with action densities that match known one- and two-soliton results and suggest new building blocks for ASDYM soliton classification.
Fr\"olicher-Nijenhuis geometry and integrable matrix PDE systems
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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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Soliton Resonances in Four Dimensional Wess-Zumino-Witten Model
Double-pole and V-shape resonance soliton solutions are constructed for the U(2) Yang equation on ultrahyperbolic space, with action densities that match known one- and two-soliton results and suggest new building blocks for ASDYM soliton classification.