Abstract
The modulation of a dust-ion acoustic wave (DIAW) in dusty plasmas with the combined effects of bounded cylindrical geometry and the transverse perturbation are studied. By using the standard reductive perturbation method, a cylindrical Davey–Stewartson (CDS) equation is obtained for the first time. The modulational instability of the DIAW described by the CDS equation is investigated. A new explicit criterion for the modulational instability of the DIAW described by the CDS is obtained. It is shown that the present instability criterion is different from that obtained in a standard nonlinear Schrödinger equation (NLSE), a Davey–Stewartson equation, or a cylindrically symmetric NLSE, and a wider parameter domain for modulational instability exists.
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