Conditions for the existence of ion-acoustic solitary waves are investigated in a cold collisionless plasma taking into account the electron inertia. The Sagdeev’s pseudopotential is derived in terms of u, the ion velocity. It is found that there exists a critical value of u0(≠0), the value of u at which (u′)2=0, beyond which the soliton solution ceases to exist and the electron inertia plays a non-insignificant role in determining this critical value. This result reproduces the result of Johnston and Epstein [Phys. Plasmas. 7, 906 (2000)] when the effect of electron inertia is neglected.

Dust ion-acoustic soliton is studied in an electron-dust-ion plasma by employing a two-fluid quantum hydrodynamic model. Ions and electrons are assumed to follow quantum mechanical behaviors in dust background. The Korteweg–de Vries (KdV) equation and higher order contribution to KdV equations are derived using reductive perturbation technique. The higher order contribution is obtained as a higher order inhomogeneous differential equation. The nonsecular solution of the higher order contribution is obtained by using the renormalization method and the particular solution of the inhomogeneous equation is determined using a truncated series solution method. The effects of dust concentration, quantum parameter for ions and electrons, and soliton velocity on the amplitude and width of the dressed soliton are discussed.

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