Spin electron acoustic soliton: Separate spin evolution of electrons with exchange interaction

Separate spin evolution quantum hydrodynamics is generalized to include the Coulomb exchange interaction. The Coulomb exchange interaction is considered as the interaction between the spin-down electrons being in the quantum states occupied by one electron, giving main contribution in the equilibrium. The generalized model is applied to study the non-linear spin-electron acoustic waves. Existence of the spin-electron acoustic soliton is demonstrated. Contributions of the concentration, spin polarization, and exchange interaction in the properties of the spin electron acoustic soliton are studied.