Nonlinear nanostructures in the quantum electron-ion gas

In recent years, a huge number of works have been devoted to the investigation of collective behavior of quantum Fermi gas. Such interest is motivated by its potential application in modern technology, e.g. metallic and semiconducting nanostructures – such as metallic nanoparticles, metal clusters, thin metal films, spintronics, nanotubes, quantum well and quantum dots, nanoplasmonic devices, quantum X-ray free – electron lagers, etc. To be based on the new quantum kinetic equation of Fermi particles, which recently was derived by N. L. Tsintsadze and L. N. Tsintsadze [1], a general quantum dispersion equation for electron-ion degenerate Fermi gas, with Madelung term is derived and studied for some interesting cases. Furthermore, then Korteweg-de Vries (KdV) equation for novel quantum waves is derived and contribution of KdV solitons are discussed. New effect that we have shown is that when the quantum (Madelung) term exceeds the term due to the charge separation, the compressional becomes the rarefunction solitons.