Completely Localized Stable Elliptic and Vortex Solitons in Magnetized Dusty Plasma

Abstract

We numerically and theoretically investigated the elliptic and vortex solitons, and their dynamical stabilities in a magnetized dusty plasma. By using the Petviashvili method, a type of completely localized solitons, which are also confirmed analytically, is found numerically. Numerical results indicate that the amplitude is proportional to its velocity and inverse proportional to the nonlinear interaction strength. The linear stability analysis shows that these solitons are always linearly stable, which agrees well with the nonlinear dynamic evolution. Finally, we find that both elastic and inelastic collisions exist when two localized solitons collide. It is an elastic one when the collision occurs between a localized soliton and a stable line soliton. However, a series of localized solitons will be excited if a localized soliton and an unstable line soliton collide, suggesting that inelastic collisions also exist. This finding may be helpful to understand the nonlinear phenomena in magnetized dusty plasma.