Nonlocal Equations of Schroedinger Type for Langmuir Waves in Vlasov Plasmas

Modified nonlocal Schroedinger equation was derived in the framework of the kinetic description of plasmas by means of the hierarchy equation method and due to asymptotic expansion with respect to the frequency inverse. The derived equation is different from the ordinary NLS equation by occurrence of an additional nonlocal integral term. The fundamental features of the equation are demonstrated. In particular, the correspondence between solutions of the equation and the Zakharov solutions of the NLS equation is considered. (author)