Integrability in string theory and m-theory

In this paper we will demonstrate two facts indicating the existence of an analogue of integrability for three- dimensional systems, in particular the M2-brane in M-theory. To do this, we will consider the natural formulation of three-dimensional systems in terms of the Nambu bracket and its connection with the generalized Yang-Baxter equation. We will discuss Yang-Baxter deformations that preserve the integrability of sigma models and in which the classical Yang-Baxter equation naturally arises. We will then present a generalization of the Yang-Baxter deformations to the M-theory case, in which a generalized Yang-Baxter equation arises in a similar way.