Dynamical behavior of the soliton formation and propagation in magnetized plasma

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Abstract
Despite many theoretical studies on soliton formation and its propagation in plasmas, no study with multicomponent magnetized plasma has derived the special nonlinear wave equation, called the Zakharov–Kuznetsov equation [V. E. Zakharov and E. A. Kuznetsov, Sov. Phys. JETP 39, 285 (1974)]. Thus, the main emphasis has been given to employing the hyperbolic-type method for finding the soliton features in relation to laboratory and space plasma environments. Where this method has been unsuccessful, an alternate method has been developed to yield the soliton propagation. The features of the nonlinear plasma-acoustic waves, which depend on the plasma composition, affect the coexistence of compressive and rarefactive solitary waves. Later, allowing for the higher order nonlinearity in the dynamics, one is led to further different solitary waves along with double layers. The main aim of the present study is to use a new formalism for finding the soliton propagation from the nonlinear wave equation with strong, as well as weak, nonlinearity. The coexistence of different nonlinear acoustic modes due to the interaction of multiple charges in plasma is shown. Moreover, the theoretical observations revealed many other soliton-like structures, which could be similar to the dip and hump solitons observed by the Freja Scientific Satellite and the collapsed solitons expected in the propagation of solar flares, as well as in the interplanetary space plasmas.