Asymptotic Equivalence Between Quasi-Grammian and Quasi-Wronskian N-Soliton Solutions of the Anti-Self-Dual Yang-Mills Equation

2026/07/20 by Shan-Chi Huang · 1 voice
#nlin.SI #hep-th #math-ph #math.MP

paper · pdf

Abstract

Asymptotic equivalence between the quasi-Grammian and quasi-Wronskian representations of N-soliton solutions in the J-matrix formulation of the anti-self-dual Yang-Mills (ASDYM) equation is established up to a constant matrix factor. This formulation, known as the Yang equation, serves as the equation of motion of the four-dimensional Wess-Zumino-Witten (WZW₄) model and is equivalent to the ASDYM equation. To visualize the solitonic behavior, the action density of the WZW₄ model is evaluated for G=U(2), demonstrating that the quasi-Grammian and quasi-Wronskian representations exhibit the same asymptotic soliton profiles, while the phase shift factors associated with N-soliton collisions are obtained explicitly. Hence, by virtue of the particle-like nature of solitons, the two representations describe the same class of ASDYM N-soliton solutions. These solitons can be regarded as a four-dimensional analogue of KP/KdV-type multi-solitons in fluid dynamics, suggesting a possible connection between the ASDYM equation and higher-dimensional Sato theory. Exact quasi-Grammian N-soliton solutions are also presented for N≤4.

Citations

• Integrability and transformations in the bilinear method: An introduction
• Perturbative Gauge Theory as a String Theory in Twistor Space
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

Discussions

• Shan-Chi Huang: Asymptotic Equivalence Between Quasi-Grammian and Quasi-Wronskian $N$-Soliton Solutions of the Anti-Self-Dual Yang-Mills Equation https://arxiv.org/abs/2607.17749 https://arxiv.org/pdf [bsky, 0 points, 0 comments]

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