Complex interactions of breathers

We present our recent theoretical and experimental advancements in studying complex multiple nonlinear interactions of coherent solitary wave structures on unstable background – breathers. We use the focusing one-dimensional nonlinear Schrödinger equation (NLSE) as a theoretical model. First, we describe the nonlinear mutual interactions between a pair of co-propagative breathers called breather molecules. Then with the novel approach of breather interaction management, we adjust the initial positions and phases of several breathers to observe various desired wave states at controllable moments of evolution. Our experiments carried out on a light wave platform with a nearly conservative optical fiber system accurately reproduce the predicted dynamics. In addition, we consider generalizations of the scalar breathers theory to the vector two-component NLSE describing polarized light and show examples of resonance vector breathers transformations.