In contrast to string sigma models which are well-known to be (classically) integrable in certain backgrounds, most famously flat space or AdS(5) x S(5), the same is not true for the membrane sigma model. Reasons for this are the non-trivial gravity on the world-volume but also the rarity of three-dimensional integrable field theories in general. Here, I will present the novel observation that a certain decoupling limit of the membrane in certain backgrounds will lead to an integrable model, the Manakov-Zakharov-Ward model -- a known three-dimensional, but non-relativistic, integrable field theory. An example of backgrounds in which this limit is possible is the 11d uplift of the pure NS-NS AdS(3) x S(3) x T(4) background.
