Hopf maps as static solutions of the complex eikonal equation

Abstract

We demonstrate that a class of torus-shaped Hopf maps with arbitrary linking number obeys the static complex eikonal equation. Further, we explore the geometric structure behind these solutions, explaining thereby the reason for their existence. As this equation shows up as an integrability condition in certain non-linear field theories, the existence of such solutions is of some interest.

13 pages, slight changes in presentation, one paragraph on the symmetries of the eikonal equation added. Version accepted for publication in JMP

References in corpus (2)

• Integrability and Conformal Symmetry in Higher Dimensions: A Model with Exact Hopfion Solutions
• Ring-shaped exact Hopf solitons

Cited by in corpus (13)

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• Generalized Eikonal Knots and New Integrable Dynamical Systems
• Generalized integrability conditions and target space geometry
• New Integrable Sectors in Skyrme and 4-dimensional CP^n Model
• Symmetries of generalized soliton models and submodels on target space $S^2$
• Knotted Configurations with Arbitrary Hopf Index from the Eikonal Equation
• A first integration of some knot soliton models
• Knots, Braids and Hedgehogs from the Eikonal Equation
• Comment on ``Reduction of static field equation of Faddeev model to first order PDE'', arXiv:0707.2207
• The symmetries of the Dirac--Pauli equation in two and three dimensions