Kadomtsev-Petviashvili equation for magnetosonic waves in Hall plasmas and soliton stability

In this article we study nonlinear waves in Hall plasmas. We consider magnetosonic waves propagating at the angles with respect to the equilibrium magnetic field that are not close to either 0 or π/2. Using the reductive perturbation method we derive the three-dimensional Kadomtsev-Petviashvili (KP) equation. We use the KP equation to show that both fast and slow magnetosonic solitons are unstable with respect to transverse perturbations. We confront our results with the investigation of soliton stability in anisotropic media using the study of soliton self-refraction.