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Cauchy matrix approach to the SU(2) self‐dual Yang–Mills equation
Author(s) -
Li Shangshuai,
Qu Changzheng,
Yi Xiangxuan,
Zhang Dajun
Publication year - 2022
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12488
Subject(s) - mathematics , cauchy matrix , matrix (chemical analysis) , matrix differential equation , sylvester equation , matrix difference equation , cauchy distribution , dual (grammatical number) , class (philosophy) , mathematical analysis , mathematical physics , pure mathematics , riccati equation , differential equation , cauchy boundary condition , physics , eigenvalues and eigenvectors , boundary value problem , quantum mechanics , art , materials science , literature , artificial intelligence , computer science , composite material , free boundary problem
The Cauchy matrix approach is developed to solve theSU ( 2 ) $\mathbf {SU}(2)$ self‐dual Yang–Mills (SDYM) equation. Starting from a Sylvester matrix equation coupled with certain dispersion relations for an infinite number of coordinates, we derive some new relations that give rise to the SDYM equation under Yang's formulation. By imposing further constraints on complex independent variables, a broad class of explicit solutions of the equation under Yang's formulation are obtained.