Linear and nonlinear quantum dust ion acoustic wave with dust size distribution effect

Both linear and nonlinear quantum dust ion acoustic waves (QDIAWs) are analyzed using two fluid quantum hydrodynamics model including the dust size distribution (DSD) effect. Two different DSD functions are applied (the power law DSD and the polynomial DSD). A new dispersion relation is derived. Using the reductive perturbation technique, a quantum Zakharov-Kuzentsov equation is evaluated for the QDIAW description. The relevance of the wave velocity, amplitude, and width to the DSD and quantum effects is illustrated both analytically and numerically. Moreover, it is found that both linear and nonlinear wave properties are affected by increasing the matter density; the more dense the material the less the wave frequency. The accuracy of controlling coefficients presented in the polynomial DSD is examined numerically for both linear and nonlinear QDIAWs. A brief conclusion is presented to the current findings and their relevance to astrophysics data is also discussed. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3422551]