In general case LLE  (2) is nonintegrable. But it admits the two integrable reductions:
: a) in the 1+1 dimensions, that is Eq. (3), it is integrable
: b) when . In this case the (1+1)-dimensional LLE (3) turns into the continuous classical Heisenberg ferromagnet equation (see e.g. Heisenberg model (classical)) which is already integrable.