Nonlinear theory of the isothermal ion-acoustic waves in the warm degenerate plasma

The collisionless unmagnetized degenerate plasma with zero-temperature components is considered. The exact barometric formulas for the electron and ion degenerate gases and the exact expressions for the electron and ion Debye radii are derived. A dispersion relation for the isothermal ion-acoustic waves is obtained and analyzed and an exact solution for the linear velocity of the ion sound is found. The domains of parameters in which the soliton solutions can be found are determined using the analysis of the dispersion relation. The nonlinear theory of the isothermal ion-acoustic waves is developed and employed to obtain and to analyze the exact solution of the original equations. The analysis is based on the method of the Bernoulli pseudopotential. The ranges of the phase velocities of the periodic ion-acoustic waves and the soliton velocities are determined. It is demonstrated that the ranges are not overlapped and that the soliton velocity cannot be less than the linear velocity of the ion sound. The profiles of physical quantities in the periodic wave and soliton are constructed.