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Abstract
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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.
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