New solitons and conditional stability to the high dispersive nonlinear Schrodinger equation with parabolic law nonlinearity

The complete discrimination system was proposed to search traveling wave solutions for a (1 + 1)-dimensional nonlinear Schrodinger equation with parabolic law nonlinearity. As a consequence, we obtained a series of solutions which contain dark soliton, bright soliton, triangular solitary wave solution, kink soliton, periodic solutions and implicit analytical solutions. At the same time, numerical simulations were demonstrated to visualize the mechanics of these solutions. Lastly, linear stability of dark soliton u(25) in Lyapunov's sense was discussed.

Automated summary

In this study, a complete discrimination system was proposed to search traveling wave solutions for a (1 + 1)-dimensional nonlinear Schrodinger equation with parabolic law nonlinearity. Various solutions including dark soliton, bright soliton, triangular solitary wave solution, kink soliton, periodic solutions and implicit analytical solutions were obtained, and their mechanics were visualized through numerical simulations. Additionally, the linear stability of dark soliton u(25) in Lyapunov's sense was discussed.