Localized solitary waves and their dynamical stabilities in magnetized dusty plasma

We consider a magnetized dusty plasma, which composed of low-temperature and high-temperature ions, electrons, and dust particles. The dynamical behaviors can be described by a (3+1)-dimensional Zakharov-Kuznetsov equation (ZKE). Interestingly, a type of completely localized solitary waves, which are different from the line solitons, of ZKE are obtained analytically and approximately for the first time. This kind of solitary wave is also confirmed numerically by the Petviashvili method. Both the analytical and numerical results indicate that the amplitude of the localized wave is proportional to its velocity and inverse proportional to the nonlinear interaction strength. A finite difference scheme with second-order accuracy is presented to make the long-time nonlinear evolution of ZKE. The numerical results indicate that the localized solitons are always dynamically stable. Moreover, the collision between two solitary waves is investigated numerically. The results show that both elastic and inelastic collision exist when two localized solitary waves colliding.