Unified derivation of Korteweg-de Vries- Zakharov-Kuznetsov equations in multispecies plasmas

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Abstract
Ordinary, modified and mixed Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equations governing the oblique propagation of electrostatic modes in magnetized plasmas have been (re)derived in a fully systematic way for general mixtures of hot isothermal, warm adiabatic fluid and cold immobile background species. The ordinary KdV-ZK equation is the standard paradigm, but for more complicated plasma compositions the soliton character can switch from compressive to rarefactive or vice versa, at critical densities and temperatures. For these special values the modified KdV-ZK equation is to be used, whereas near such critical values a mixed KdV-ZK equation can model double layers. Since the description is given in physical rather than normalized variables for genuine multispecies plasmas, widely different frequency regimes and plasma models can be treated and the general features compared. Applications include electron- and ion-acoustic modes in normal plasmas with one or two hot Boltzmann electron species, or ion- and dust-acoustic modes in dusty plasmas, depending on how the heavier components are modelled. Special emphasis is given to a discussion of critical regimes for the better known plasma electrostatic modes, leading to new results and better physical insight.