Abstract
With the aid of the planar dynamical systems and invariant algebraic cure, all algebraic traveling wave solutions for two extended (2 + 1)-dimensional Kadomtsev-Petviashvili equations, which can be used to model shallow water waves with weakly nonlinear restoring forces and to describe waves in ferromagnetic media, were obtained. Meanwhile, some new rational solutions are also yielded through an invariant algebraic cure with two different traveling wave transformations for the first time. These results are an effective complement to existing knowledge. It can help us understand the mechanism of shallow water waves more deeply.