Cylindrical and spherical dust ion-acoustic Gardner solitons in a quantum plasma

The properties of nonplanar (cylindrical and spherical) quantum dust ion-acoustic (QDIA) solitary waves in an unmagnetized quantum dusty plasma, whose constituents are inertial ions, Fermi electrons with quantum effect, and negatively charged immobile dust particles, are investigated by deriving the modified Gardner (MG) equation. The reductive perturbation method is employed to derive the MG equation, and the basic features of nonplanar QDIA Gardner solitons (GSs) are analyzed. It has been found that the basic characteristics of GSs, which are shown to exist for the value of Z(d)n(d0)/n(i0) around 2/3 (where Z(d) is the number of electrons residing on the dust grain surface, and n(d0) and n(i0) are, respectively, dust and ion number density at equilibrium), are different from those of the Korteweg-de Vries solitons, which do not exist for the value of Z(d)n(d0)/n(i0) around 2/3. It is also seen that the properties of nonplanar QDIA GSs are significantly different from those of planar ones. (C) 2011 American Institute of Physics. [doi:10.1063/1.3646738]