  I consider electrodynamics and the problem of knotted solitons in
two-component superconductors. Possible existence of knotted solitons in
multicomponent superconductors was predicted several years ago. However their
basic properties and stability in these systems remains an outstandingly
difficult question both for analytical and numerical treatment. Here I propose
a new perturbative approach to treat self-consistently all the degrees of
freedom in the problem. I show that there exists a length scale for a Hopfion
texture where the electrodynamics of a two-component superconductor is
dominated by a self-induced Faddeev term, which is a stark contrast to the
Meissner electrodynamics of single-component systems. I also show that at
certain short length scales knotted solitons in two-component Ginzburg-Landau
model are not described by a Faddeev-Skyrme-type model and are unstable.
However these solitons can be stable at some intermediate length scales. I
argue that configurations with a high topological charge may be more stable in
this system than low-topological-charge configurations. In the second part of
the paper I discuss qualitatively different physics of the stability of knotted
solitons in a more general Ginzburg-Landau model and point out the physically
relevant terms which enhance or suppress stability of the knotted solitons.
With this argument it is demonstrated that the generalized Ginburg-Landau model
possesses stable knotted solitons.
