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.
Solutions to the SU($\mathcal{N}$) self-dual Yang-Mills equation
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abstract
In this paper we aim to derive solutions for the SU($\mathcal{N}$) self-dual Yang-Mills (SDYM) equation with arbitrary $\mathcal{N}$. A set of noncommutative relations are introduced to construct a matrix equation that can be reduced to the SDYM equation. It is shown that these relations can be generated from two different Sylvester equations, which correspond to the two Cauchy matrix schemes for the (matrix) Kadomtsev-Petviashvili hierarchy and the (matrix) Ablowitz-Kaup-Newell-Segur hierarchy, respectively. In each Cauchy matrix scheme we investigate the possible reductions that can lead to the SU$(\mathcal{N})$ SDYM equation and also analyze the physical significance of some solutions, i.e. being Hermitian, positive-definite and of determinant being one.
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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.