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

Dissipative shocks and solitons in Pair-ion PlasmasThe stretching of the independent variables for 2-D electrostatic waves in PIplasmas is defined as1/ 2ξ = ε ( x − λt),χ = εy,τ = εNow collecting the terms of different powers of ε, we finally obtained the KPB equationas follows∂ ⎛ ∂ϕ⎜ +∂ξ⎝ ∂τ3∂ϕ∂ ϕAϕ+ B − C3∂ξ∂ξwhere the coefficients as defined as,3 / 222∂ ϕ ⎞ ∂= 02⎟ + ϕD2∂ξ⎠ ∂χt(20)A =B =2 2[3λ−1)(λ − β )2 222λ(λ −1)(λ − β )[( λ −1)2 2 2 2( λ −1)( λ − β )22λ[(λ −1)232+ ( λ − β )22− (3λ− β )( λ −1)2]232+ ( λ − β )]2](Nonlinear coefficient)(Dispersive coefficient)Cη=0+2( λ − β )22[( λ −1)D = λ / 222−η0−2( λ −1)2+ ( λ − β )2]2(Dissipative coefficient)(weakly dispersive coefficient)29