Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
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Double layer <strong>in</strong> Pair-<strong>ion</strong> Plasmas (contd.)The mKdV equat<strong>ion</strong> is described asA ∂τϕ23 31+ Q ∂ξϕ1+B ∂ξϕ1+ ∂ξϕ1=0(14)where the coefficients are def<strong>in</strong>ed asB= ⎡ 1 1 ⎤A 2λ⎢+2 2 2 ⎥⎣(λ − μ)( λ −1)2⎦2⎡⎛ 2 1 ⎞⎛ 2 μ ⎞⎢⎜ 2 λ − ⎟⎜ 2 λ −2 22 2⎟⎢ (3λ− 1) ⎝ 3 ⎠ (3λ− 1)= −+−⎝ 3 ⎠2 52 42524⎢ 2 ( λ − 1) ( λ − 1) 2 ( λ − μ ) ( λ − μ )⎢⎣22(3λ− μ)(3λ−1)Q = −2 3 2 32( λ − μ)2( λ −1)2⎤⎥⎥⎥⎥⎦Now us<strong>in</strong>g the transformat<strong>ion</strong>η = ξ −Uτthe above mKdV equat<strong>ion</strong>22