Theory of a spatially periodic bose condensate in the weakly nonideal Bose gas model

The possibility of constructing the theory of a spatially periodic Bose condensate in the weakly nonideal Bose gas model is studied. The concept of quasi means and the related separated Bose condensate method are used to derive equations for determining the spatially periodic order parameter for zero temperature at which the contribution of quasiparticles to the thermodynamics of the boson system can be neglected. One-period solutions of these equations are found. Questions of thermodynamic stability are considered for a spatially periodic Bose condensate.