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In a sequel to a recent work [Das, Sarma, and Talukdar, Phys. Plasmas 5, 63 (1998)], the different nonlinear plasma-acoustic waves, based on the fluid approximation, have been derived showing the coexistences of dust-acoustic waves in plasmas contaminated by dust-charged grains. The features of the nonlinear waves, depending on the plasma composition, describe various natures of solitary waves. A new formalism, known as the tanh method and stemming from the modified simple wave solution technique, has been developed for finding the soliton propagation in the nonlinear plasma wave dynamics. The method is straightforward, with minimal mathematical manipulation, finding the heuristic formation and propagation of ion-acoustic solitary waves in the dusty plasma. The main aim is, based on the tanh method, to revisit the results in a simpler case and extending them to explain the behavior of higher-order nonlinear waves derived in generalized multicomponent plasmas. The theoretical observations highlight the salient features of nonlinear waves coexisting with the dust-acoustic wave. The new findings might expect the effect, because of the dust-charged grains, to be the common feature of nonlinear waves in the dusty plasmas, and could be of interest for future experiments in laboratory as well as in space plasmas.

A three-dimensional nonlinear Kadomtsev–Petviashvili (K–P) wave equation is derived to discuss the solitons in multicomponent plasma contaminated with negative ions. A new formalism of the simple wave solution method is developed for finding the soliton behaviors caused by the presence of negative ions in plasmas. It is seen that the nonlinear wave equation leads, in some cases, to an ordinary differential equation and a straight way for solving the soliton propagation in plasmas. The overall observations describe the natures of compressive and rarefactive solitons along with the shock-like wave caused by the interaction of negative ions. Also discussed are the possible controls of the scenarios of soliton behaviors. Moreover it is believed, from present investigations, that the observations of collapses or explosions in solitons could enhance the understanding of the soliton phenomena in laboratory and space plasmas.

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Using the well-known reductive perturbation technique, the three-dimensional (3D) Burgers equation and modified 3D Burgers equation have been derived for a plasma system comprising of non-thermal ions, Maxwellian electrons, and negatively charged fluctuating dust particles. The salient features of nonlinear propagation of shock waves in such plasmas have been investigated in detail. The different temperature non-thermal ions and Maxwellian electrons are found to play an important role in the shock waves solution. The analytical solution of the 3D Burgers equation and modified 3D Burgers equation ratifying the propagation of dust acoustic shock waves are derived using the well-known tanh method. On increasing the population of non-thermal ions, an enhancement in the amplitude of shock waves is seen for negatively charged dust particles. A striking dependence of amplitude and width of shock waves on the ratio of ion temperatures and densities are also reported. Finally we introduced a new stretching coordinate and perturbation for the nth-order nonlinear 3D Burgers equation and its solution by the use of the tanh method. We found that, due to higher nonlinearity, the amplitude of shock waves decreases while width remains constant for all plasma parameters considered in the present investigation. The features accounted here could be relevant in the case of different space and astrophysical plasmas and laboratory dusty plasma for negatively charged dust fluctuation.