Taming non-linear waves
Most natural systems are nonlinear and are modelled by nonlinear systems of equations. The essential difference between linear and nonlinear systems is that the first satisfy a simple superposition principle. This superposition principle allows the solution of linear systems to be broken into pieces that can be solved independently. Despite the difficulty caused by the lack of the superposition principle, the 'Nonlinearity management of atomic and optical systems' (NOMATOS) project team have made significant progress in solving nonlinear systems. Their research work started with non-linear effects in waveguides. As the name implies, waveguides "guide" information in the form of electromagnetic waves between two points in telecommunication networks. The NOMATOS researchers then turned to matter waves in clouds of Bose-Einstein condensates. A Bose-Einstein condensate represents the most "classical" form of matter waves, just like an optical laser emits the most classical form of electromagnetic waves. There are no ordinary words to describe them, because they come from the quantum world. They are formed of objects behaving as both particles and waves — a strange duality described by Schrödinger's equations. The NOMATOS researchers introduced a system of nonlinear Schrödinger's equations, a model which can be realised in a Bose-Einstein condensate. They identified regions of stability for discrete symmetric solitons. The existence of several types of solitary travelling waves which are solutions of the nonlinear Schrödinger's equations was demonstrated. These ranged from uniform to very fragmented chains of solitons. More importantly, NOMATOS researchers found that localised dissipation of wave energy can be an effective tool for managing soliton waves. These findings were published in international scientific journals and opened up new lines of research in nonlinear physics. The joint publications also evidence the successful links established with members of the international scientific community.
Keywords
Waves, Bose-Einstein condensates, nonlinear systems, waveguides, telecommunication, networks, matter waves, electromagnetic, solitons, Schrödinger's
