Аннотация:Abstract—Three nonlinear equations for ion acoustic and drift waves in a plasma are derived. The fun-damental solution of the common linear part of the resulting nonlinear equations is constructed, andits smoothness properties are studied. Next, the second Green formula in a bounded domain is con-structed, which is then used to derive the third Green formula in a bounded domain. Finally, two vari-ants of the third Green formula in the entire space are constructed in a certain class of functions.