DIRAC OPERATOR ON A CONFORMAL SURFACE IMMERSED IN ℝ4: A WAY TO FURTHER GENERALIZED WEIERSTRASS EQUATION

DOI10.1142/S0129055X00000149zbMath0965.53009OpenAlexW2070264474MaRDI QIDQ4519841

Shigeki Matsutani

Publication date: 4 December 2000

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129055x00000149

zbMATH Keywords

Dirac operatornonlinear Schrödinger equationLax operatormodified Novikov-Veselov equationgeneralized Weierstrass equation

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05)

Related Items (4)

Dirac equation on a curved surface ⋮ On the Moduli of a Quantized Elastica in ℙ and KdV Flows: Study of Hyperelliptic Curves as an Extension of Euler's Perspective of Elastica I ⋮ No existence of the geometric potential for a Dirac fermion on a two-dimensional curved surface of revolution ⋮ On a discretization of asymptotic nets

Cites Work

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• Statistical mechanics of non-stretching elastica in three-dimensional space
• An elementary geometric characterization of the integrable motions of a curve
• On the physical relation between the Dirac equation and the generalized mKdV equation on a thin elastic rod
• GENERALIZED WEIERSTRASS-ENNEPER INDUCING, CONFORMAL IMMERSIONS, AND GRAVITY
• PHYSICAL REALIZATION OF THE JIMBO-MIWA THEORY OF THE MODIFIED KORTEWEG-DE VRIES EQUATION ON A THIN ELASTIC ROD: FERMIONIC THEORY
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• IMMERSION ANOMALY OF DIRAC OPERATOR ON SURFACE IN ℝ³
• The Korteweg–de Vries hierarchy as dynamics of closed curves in the plane
• General Relativity in Terms of Dirac Eigenvalues
• A soliton on a vortex filament

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