Generalized Sagdeev approach to nonlinear plasma excitations

In this work, we extend the Sagdeev pseudopotential approach by introducing the generalized potential, which is used for the investigation of nonlinear periodic, solitary, as well as double layer excitations in plasmas. Particularly in the framework of the generalized potential, the nonlinear excitations are investigated based on their total Sagdeev pseudoenergy. In this framework, conventional solitons are categorized as species with zero Sagdeev energy. A new type of positive energy solitons with subsonic Mach numbers is found. It is remarked that positive energy solitons do not obey the standard behavior of KdV solitons. Different types of nonlinear excitations are characterized in terms of their Sagdeev energy, and the parametric regions in which they exist are studied in detail. The nonlinear periodic waves are found to be either negative or positive energy type, characteristics of which are found to be quite different. A small amplitude theory of Sagdeev cnoidal waves is developed, which can be used to investigate the low energy waves with Mach numbers close to the critical one. Using the new concept of Sagdeev energy, we study different properties of large amplitude positive and negative energy nonlinear periodic waves in a plasma with arbitrary degree of electron degeneracy ranging from dilute classical up to the completely degenerate plasmas.