Generalized Eikonal Knots and New Integrable Dynamical Systems

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.