Nonplanar ion-acoustic waves in a quantum plasma

The nonlinear properties of ion-acoustic (IA) waves in an electron-ion quantum plasma with the effects of quantum corrections are studied in a nonplanar spherical geometry. For this purpose quantum hydrodynamic model (QHD) is used and a variable coefficient Kadomtsev-Petviashvili (KP) equation is derived by using the standard reductive perturbation method. The pressures for both electrons and ions are considered in two ways: one by using the complete fluid pressure equation and other by the equation of state pertaining to a three-dimensional zero-temperature Fermi gas. It is found that of the two ways, the latter gives significant results when the nondimensional quantum diffraction parameter H approaches or nearer to unity. The important quantum mechanical effects are examined numerically on the profiles of the compressive and rarefactive solitons. It is found that H plays a significant role in the formation of compressive and rarefactive solitons. A critical value of H is also found which depends on the phase velocity of the wave and the ion to electron Fermi temperature ratio, for which the soliton formation ceases to exist. (C) 2007 Elsevier B.V. All rights reserved.