Spinor Fields on the Surface of Revolution and their Integrable Deformations via the mKdV-Hierarchy

Details Spinor Fields on the Surface of Revolution and their Integrable Deformations via the mKdV-Hierarchy Spinor Fields on the Surface of Revolution and their Integrable Deformations via the mKdV-Hierarchy

1999-06-21

arxiv.org/abs/math/9906140v1

Mathematics

Differential Geometry

15 pages, LaTeX2e

Scientific paper

Spinor fields on surfaces of revolution conformally immersed into 3-dimensional space are considered in the framework of the spinor representations of surfaces. It is shown that a linear problem (a 2-dimensional Dirac equation) related with a modified Veselov- Novikov hierarchy in the case of the surface of revolution reduces to a well-known Zakharov-Shabat system. In the case of one-soliton solution an explicit form of the spinor fields is given by means of linear Bargmann potentials and is expressed via the Jost functions of the Zakharov-Shabat system. It is shown also that integrable deformations of the spinor fields on the surface of revolution are defined by a modified Korteweg-de Vries hierarchy.

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