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New Soliton Solutions of Anti-Self-Dual Yang-Mills equations
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abstract
We study exact soliton solutions of anti-self-dual Yang-Mills equations for $G =GL(2)$ in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action density Tr$F_{\mu\nu}F^{\mu\nu}$ can be real-valued. These solitons are shown to be new type of domain walls in four dimension by explicit calculation of the real-valued action density. Our results are successful applications of the Darboux transformation developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the four-dimensional spaces are suggested to be not infinity but zero. Furthermore, whether gauge group $G= U(2)$ can be realized on our solition solutions or not is also discussed on each real space.
Forward citations
Cited by 2 Pith papers
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Asymptotic Equivalence Between Quasi-Grammian and Quasi-Wronskian $N$-Soliton Solutions of the Anti-Self-Dual Yang-Mills Equation
Quasi-Grammian and quasi-Wronskian N-soliton solutions of the ASDYM/Yang equation are asymptotically equivalent up to a constant matrix factor, with explicit N-soliton phase shifts.
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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 blo...
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