New solutions to a category of nonlinear PDEs - Li, Bacui; Wang, Fuzhang (Frontiers in Physics, 2025)
The nonlinear partial differential equations are not only used in many physical models, but also fundamentally applied in the field of nonlinear science. In order to solve certain nonlinear partial differential equation, the extended hyperbolic auxiliary equation method (EHAEM) is introduced in this article by means of the symbolic computation software. The basic idea of the new algorithm is that if certain nonlinear partial differential equation can be converted into the form of elliptic equation, then its solutions are readily obtained. By taking the generalized Schrödinger equation as an example, we demonstrate the effectiveness of the proposed algorithm. Meanwhile, many new solutions are worked out, which may be useful for depicting nonlinear physical phenomena.