Elemantary principles of nonlinear quantum mechanics

Linear quantum mechanics is a one century theory to explain physical lows in atomic world, it has great success in new technology and it has chanced many philosophical explanation of classical point of view in natural and social sciences. But recently a lots of new physical macroscopic observations have no simple explanation in linear quantum mechanics such as superconductivity, superfluity, BEC, quantum entanglement ect. On the other hand macroscopic world shows nonlinear behavior and there are many effort to do physical theory for nonlinear dynamical systems. In the literature recently there are many study about nonlinear quantum systems which is try to explain macroscopic quantum effects mentioned above. The main aim of this thesis is to review this studies and the principle of nonlinear quantum mechanics