Transformation Theory Of Nonautonomous Nonlinear Schr(?)dinger Equation

Nonlinear Schrodinger equation (NLSE) is one of most universal significance nonlinear model in modern science, which has been applied in many areas of physics, Bose-Einstein condensates (BEC), plasma physics, nonlinear optics, fluid dynamics and so on. In the past several decades, different research specialists have worked out many soliton solutions and made a comprehensive and systemic study on its propagation dynamics with different methods. However, in some real physic systems, optical communication or BEC, it always lead to nonautonomous NLSE model, which is more complicated than NLSE in form. And it have some difficulties to directly solve nonautonomous NLSE in analytic. Consequently, to study their dynamics, we only have to use numerical methods.In this paper, we transform nonautonomous NLSE into NLSE via a similarity transformation. With the algebraic relationships between the two equations above and various solutions of NLSE, we obtain the new analytical solutions of nonautonomous NLSE. Moreover, optical communication and BEC system are analyzed and discussed with the help of the similarity transformation here. Also, it gives us a new idea to reach analytical solutions of nonautonomous NLSE or homologous nonlinear equation.