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Prog. Theor. Phys. Vol. 66 No. 6 (1981) pp. 1970-1984

Sphrically Symmetric Bogomolny Equation and Corresponding One-Dimensional Lattice Model

Takao Koikawa

Department of Physics, Hiroshima University, Hiroshima 730

(Received June 29, 1981)

Abstract:

The spherically symmetric Bogomolny equation by the minimal embedding of SU(2) into SU(N + 1) reveals its relation to the well-known one-dimensional lattice model called the Toda lattice. We clarify the difference and similarity between them from the viewpoint of group theory as well as that of Hirota's bilinearization. On the basis of this comparison, we show that the even-number-soliton solutions of the Bogomolny equation can be obtained in the limit, N →∞. We give the third conserved quantity of the Bogomolny equation, which is characteristic of the soliton equations. An infinite number of conserved quantities are also shown in the continuous Toda equation: the 1 + 1-dimensional equation, which should be compared with other soliton equations.

URL : http://ptp.ipap.jp/link?PTP/66/1970/
DOI : 10.1143/PTP.66.1970

[ Full Text PDF : FREE ACCESS (525K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Journal of the Physical Society of Japan 56 (1987) pp. 3491-3498 :

   The 3+1 Dimensional Toda Equation and its Exact Solutions

   Akira Nakamura

2. Progress of Theoretical Physics Vol. 102 No. 1 (1999) pp. 29-35 :

   Soliton Formulation Using Moyal Algebra

   Takao Koikawa

3. Progress of Theoretical Physics Vol. 105 No. 6 (2001) pp. 1045-1057 :

   Soliton Equations Extracted from the Noncommutative Zero-Curvature Equation

   Takao Koikawa

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