Cylindrical and spherical quantum ion acoustic waves

Cylindrical and spherical deformed Korteweg-de Vries (dKdV) equations are derived for quantum ion acoustic waves in an unmagnetized two species quantum plasma system, comprised of electrons and ions, by the reductive perturbation technique in the weakly nonlinear limit. The properties of quantum ion acoustic solitary waves are studied taking into account the quantum mechanical effects in a nonplanar cylindrical or spherical geometry, which differs from one-dimensional planar geometry. Both analytical and numerical solutions of the dKdV equations are discussed in some detail. There exists a critical value of quantum parameters beyond which the quantum ion acoustic soliton collapses. It is also found that for the critical values of H, viz., H=2, some nontrivial analytical solution exists for both cylindrical and spherical dKdV equations. (c) 2007 American Institute of Physics.