Nonlinear Equation for Dust Drift Waves

A nonlinear equation for dust drift waves is derived assuming two-dimensional propagation and ignoring the role of dust acoustic waves. Both the nonlinear dust density term and the dust vorticity term are taken into account. If vorticity term is ignored, the equation gives two dimensional solitary waves and if density nonlinearity effect is discarded, then it reduces to Hasegawa-Mima equation for dust drift waves which admits dipole vortex solutions.