Generalized Eikonal Knots and New Integrable Dynamical Systems

Abstract

A new class of non-linear O(3) models is introduced. It is shown that these systems lead to integrable submodels if an additional integrability condition (so called the generalized eikonal equation) is imposed. In the case of particular members of the family of the models the exact solutions describing toroidal solitons with a non-trivial value of the Hopf index are obtained. Moreover, the generalized eikonal equation is analyzed in detail. Topological solutions describing torus knots are presented. Multi-knot configurations are found as well.

13 pages

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• k-defects as compactons
• Integrable theories and loop spaces: fundamentals, applications and new developments
• Investigation of the Nicole model
• Integrability from an abelian subgroup of the diffeomorphism group
• Hopf solitons and Hopf Q-balls on S^3
• Generalized integrability conditions and target space geometry
• Pullback of the Volume Form, Integrable Models in Higher Dimensions and Exotic Textures
• Conservation laws in Skyrme-type models
• Integrability and Diffeomorphisms on Target Space