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Nonlineaer wave propagation in a relativistic bounded plasma is analysed through the pseudopotential approach by taking into account the streaming of electrons, and electron inertia. The finite geometry is seen to effect both the forward moving and reflected modes of propagation. Its dependence on the electron–ion mass ratio is also critically analysed. In the second part of the paper we study the formation of solitons through the pseudopotential approach. The variation of the form of the pseudopotential is studied with respect to the radius of the bounding system, the electron–ion mass ratio, and the streaming velocity u0. It is observed that the finite geometry and electron inertia significantly affect the solitary wave formation.

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The linear and nonlinear propagation of dust-acoustic waves in a dusty plasma bounded in finite geometry has been theoretically investigated. It is found that the finite geometry of the bounded plasma makes a significant contribution to the instability of the wave. Moreover, the pseudopotential has a positive and inverted profile that prevents the trapping of particles and does not favor solitary waves in bounded dusty plasma.

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