Using the reductive-perturbation technique on the system of hydrodynamic equations for the cold magnetized ions, the Boltzmann distribution for the two distinct groups of hot electrons, and the Poisson equation, we derive a multi-dimensional modified Korteweg-de Vries equation. With appropriate boundary conditions this equation is shown to yield both soliton and double layer potential profiles.
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Bharuthram et al. (1986) studied this question.
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