Chinese Physics C > 1992, Vol. 16 > Issue(5): 408-413

Description of the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions

LI Fu-Bin^,

The Mathematical-Mechanical Department,China University of Mining Technology,Xuzhou 221008

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Abstract：
With the theory of harmonic maps and the eight-dimensional Riemannian manifold,the completely integrable SU(2) and SU(3) self-dual Yang-Mills source-free field equations are described.Sixteen independent Killing vector fields are determined,two transformation groups which map solutions into solutions are constructed,and a conjecture on the complete integrability of systems by the inverse scattering method is formulated.

References

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B. C., Xanthopoulous, J. Phys. A14(1981), 1445.[2] L. R. Eisenhart, Riemannian Gecmetry; Princeton, NJ, Princeton University Press, 1926[3] P. D. Lax, Commun. Pure. Appl. Math., 21(1968), 467.[4] A. C. Scott, E. Y. F. Chu, D. W. Melaughlin, Proc. IEEE., 61(1973), 1443.[5] P, Summers, PhD, thesis, the University of Texas at Austin, 1973.[6] F. Ernst, Phys. Rev., 167(1968), 1175.[7] D. Maison, Phys. Rev, Lett 41(1978), 521.[8] D. Maison, J. Math. Phys., 25(1979), 871.[9] B. K. Harrison, Phys, Rev. Lett., 41(1978), 1197.[10] V. A. Belinskii, V. E. Xakharov, Sov, Phys.JETP, 48(1978), 985.[11] V, A. Belinskii, V. E. Zakharov, Sov. Phys. JETP, 50(1979), 1.[12] R. A. Matzner, C. W. Misner, Phys. Rev., 154(1976), 1229.[13] F. Ernst, Phys. Rev., 168(1968), 1415.[14] G. A. Alekseyev, Proc. GrG, vol. 11(1980), 231,[15] C. Hoenselaers, J. Math, Phys., 19(1978), 539.[16] D, Kramer, Stephani H, Mac Callum M, HerIt E, Exact Solutions of Einstein's Field Equations, Cambridge: Cup, 1980.[17] W. Kinnersley, J. Math; Phys., 14(1973), 651[18] S. V, Manakov, V, E. Zakharov, Lett. Math, Phys., 5(1981), 247.[19] V. E. Zakharov, A. V. Mikhailov, Sov. Phys. -JETP, 47(1978), 1017.

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LI Fu-Bin. Description of the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions[J]. Chinese Physics C, 1992, 16(5): 408-413.

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Description of the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions

LI Fu-Bin^,

Corresponding author:LI Fu-Bin,

The Mathematical-Mechanical Department,China University of Mining Technology,Xuzhou 221008

Received Date:1900-01-01
Accepted Date:1900-01-01
Available Online:1992-05-05

Abstract:With the theory of harmonic maps and the eight-dimensional Riemannian manifold,the completely integrable SU(2) and SU(3) self-dual Yang-Mills source-free field equations are described.Sixteen independent Killing vector fields are determined,two transformation groups which map solutions into solutions are constructed,and a conjecture on the complete integrability of systems by the inverse scattering method is formulated.