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.