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A new form of coupled nonlinear evolution equation is derived for a plasma with negative ions in (2+1) dimensions. This system of equations can be considered to be an extension of the usual Davey–Stewartson equation. A modified version of reductive perturbation has been used. It is also shown that this set of equations can sustain both cnoidal type and the usual solitary wave-like solution. Such an equation can have important applications in describing nonlinear wave propagation in a dusty plasma.

Nonlinear Equation in (2+1) Dimensions for a Plasma with Negative Ions