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Dirac Operator of a Conformal Surface Immersed in R^4: Further Generalized Weierstrass Relation

Shigeki Matsutani
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Abstract

In the previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac operator defined over a conformal surface immersed in R^3 is identified with the Dirac operator which is generalized the Weierstrass- Enneper equation and Lax operator of the modified Novikov-Veselov (MNV) equation. In this article, I determine the Dirac operator defined over a conformal surface immersed in R^4, which is reduced to the Lax operators of the nonlinear Schrodinger and the MNV equations by taking appropriate limits. Thus the Dirac operator might be the Lax operator of (2+1)- dimensional soliton equation.

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Shigeki Matsutani. 1998-01-04. Dirac Operator of a Conformal Surface Immersed in R^4: Further Generalized Weierstrass Relation. https://arxiv.org/abs/solv-int/9801006

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