dorsal/arxiv
View SchemaDirac Operator of a Conformal Surface Immersed in R^4: Further Generalized Weierstrass Relation
| Authors | Shigeki Matsutani |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9801006 |
| URL | https://arxiv.org/abs/solv-int/9801006 |
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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"abstract": "In the previous report (J. Phys. A (1997) 30 4019-4029), I showed that the\nDirac operator defined over a conformal surface immersed in R^3 is identified\nwith the Dirac operator which is generalized the Weierstrass- Enneper equation\nand Lax operator of the modified Novikov-Veselov (MNV) equation. In this\narticle, I determine the Dirac operator defined over a conformal surface\nimmersed in R^4, which is reduced to the Lax operators of the nonlinear\nSchrodinger and the MNV equations by taking appropriate limits. Thus the Dirac\noperator might be the Lax operator of (2+1)- dimensional soliton equation.",
"arxiv_id": "solv-int/9801006",
"authors": [
"Shigeki Matsutani"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Dirac Operator of a Conformal Surface Immersed in R^4: Further Generalized Weierstrass Relation",
"url": "https://arxiv.org/abs/solv-int/9801006"
},
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