Korteweg-de Vries equation in a plasma with Thomas-Fermi distribution
In the context of plasma physics we propose to study a system characterized as a dense plasma, which occurs when the distance between the particles that compose it is smaller than the de Broglie's thermal wavelength. In this case, the temperature associated with the thermal motion of the particles is lower than the Fermi temperature. Thus systems become degenerate and classical statistics must give way to the Pauli Exclusion principle. Astrophysical environments, intense lasers, ultra-thin plasmas and microelectronic devices are some examples that can be studied from the perspective of dense plasmas. Initially we will build the appropriate fluid model that will allow us to derive, by perturbation, the nonlinear Korteweg-de Vries (KdV) equation. For a gas formed of electrons and ions (singularly ionized) we propose to replace the classic Boltzmman distribution, which describes the behavior of electrons, by the Thomas-Fermi distribution. As a result, new parameters appear in the KdV equation. We then expect that the structures provided as nonlinear solutions of this equation, such as Solitons and Jacob's elliptic functions (which describe so-called cnoidal waves), will change accordingly to the new parameters.