Controllable dynamical behaviors for spatiotemporal bright solitons on continuous wave background

Inspired by the mapping method and the direct method of symmetry reduction method, we present a new algorithm, nonlinear Schrodinger equation-based constructive method, to solve complex nonlinear evolution equations. This method can easily construct infinite solutions of the complex nonlinear evolution equations from abundant solutions of the nonlinear Schrodinger equation, including multi-soliton solutions with and without continuous wave background, rational solutions and periodic solutions, and so on. With the aid of symbolic computation, we choose (2+1)-dimensional and (3+1)-dimensional variable-coefficient nonlinear Schrodinger equations to illustrate the validity and advantages of the proposed method. According to exact solutions, we also graphically discuss some interesting soliton-like wave dynamic behaviors, which may be observable in the future experiments. These results are helpful to increase the bit-rate of optical communication.