1999/06/21 by В. В. Варламов, Vadim V. Varlamov, Varlamov, Vadim V.
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math.DG
paper · pdf · doi:10.48550/arxiv.math/9906140
15 pages, LaTeX2e
arxiv created 1999/06/21 · openalex publication_date 1999/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.