Non-linear electrostatic waves in pair-ion plasmas - National Centre ...

6. Dissipative shocks and solitons in Pair-ion PlasmasKadomstev-Petviashvili-Burgers (KPB) Equation in PI PlasmasElectrostatic structures are studied in unmagnetized, weakly dissipative PI plasmas inthe presence of weak transverse perturbations.The dissipation in the system is incorporated by taken into account the kinematicviscosity of both the species.Normalized set of dynamic equations are written as(Continuity equation for +veions)(Momentum equations for+ve ions)(Continuity equation for -veions)(Momentum equations for-ve ions)u∂n+∂t∂ ∂+ ( n+u+) + ( n+v+) = 0∂x∂y∂u∂uϕ 1 ∂n2∂+ ++ ∂+++ u++ v+= − − + η+ 2∂t∂x∂y∂xn+∂x∂x2∂ v+ ∂v+∂v+∂ϕ1 ∂n+∂ u++ u++ v+= − − + η+ 2∂t∂x∂y∂yn+∂y∂y∂u−∂t∂v∂t−∂n−∂t+ u+ u−−∂ ∂+ ( n−u−) + ( n−v−) = 0∂x∂y∂u−∂x∂v∂x−+ v+ v−−∂u−∂y∂v∂y−2∂ϕβ ∂n−∂ u−= − + η− 2∂xn−∂x∂x2∂ϕβ ∂n−∂ v= − + η−2∂yn ∂y∂y−∂u−27