  We consider bosonic subsectors of the q-deformed AdS_5 x S^5 superstring
action and study the classical integrable structure of anisotropic
Landau-Lifshitz sigma models (LLSMs) derived by taking fast-moving limits. The
subsectors are 1) deformed AdS_3 x S^1 and 2) R x deformed S^3. The cases 1)
and 2) lead to a time-like warped SL(2) LLSM and a squashed S^3 LLSM,
respectively. For each of them, we construct an infinite number of non-local
conserved charges and show a quantum affine algebra at the classical level.
Furthermore, a pp-wave like limit is applied for the case 1). The resulting
system is a null-like warped SL(2) LLSM and exhibits a couple of Yangians
through non-local gauge transformations associated with Jordanian twists.
