Spatiotemporal self-similar solutions of the generalized (3+1)-dimensional nonlinear Schr?dinger equation with polynomial nonlinearity of arbitrary order

摘要

We construct analytical self-similar solutions for the generalized (3+1)-dimensional nonlinear Schr?dinger equation with polynomial nonlinearity of arbitrary order. As an example, we list self-similar solutions of quintic nonlinear Schr?dinger equation with distributed dispersion and distributed linear gain, including bright similariton solution, fractional and combined Jacobian elliptic function solutions. Moreover, we discuss self-similar evolutional dynamic behaviors of these solutions in the dispersion decreasing fiber and the periodic distributed amplification system.