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For two-dimensional unmagnetized dusty plasmas with many different dust grain species, a Kadomtsev–Petviashvili (KP) equation, a modified KP (mKP) equation and a coupled KP(cKP) equation for small, but finite amplitude dust-acoustic solitary waves are obtained for different physical conditions respectively. The influence of an arbitrary dust size distribution described by a polynomial expressed function on the properties of dust-acoustic solitary waves is investigated numerically. How dust size distribution affects the sign and the magnitude of nonlinear coefficient A (D) of KP (mKP) equation is also discussed in detail. It is noted that whether a compressive or a rarefactive solitary wave exists depends on the dust size distribution in some dusty plasmas.

Taking into account the combined effects of the external magnetic field, adiabatic dust charge fluctuation and collisions occurring between the charged dust grains and neutral gas particles (dust-neutral collisions), the dust-acoustic solitary waves in three-dimensional uniform dusty plasmas are investigated analytically. By using the reductive perturbation method, the Korteweg–de Vries (KdV) equation governing the dust-acoustic solitary waves is obtained. The present analytical results show that only rarefactive solitary waves exist in this system. It is also found that the effects of the wave vector along the z-direction, dust charge variation, collisional frequency, the plasma density, and temperature ratio can significantly influence the characteristics of low-frequency wave modes. Moreover, for the collisional dusty plasmas, there is a certain critical value μc of the plasma density ratio μ, if μ < μc, the width of the waves increases with μ, otherwise the width of waves decreases with μ.

A modified Zakharov–Kuznetsov equation for small but finite amplitude dust acoustic waves in a magnetized votex-like ion distribution dusty plasma is obtained in this paper. It seems that there are instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable.

We discuss the possible nonlinear waves of atomic matter wave in a Bose–Einstein condensate. One and two of two-dimensional (2D) dark solitons in the Bose–Einstein condensed system are investigated. A rich dynamics is studied for the interactions between two solitons. The interaction profiles of two solitons are greatly different if the angle between them are different. If the angle is small enough, the maximum amplitude during the interaction between two solitons is even less than that of a single soliton. However, if the angle is large enough, the maximum amplitude of two solitons can gradually attend to the sum of two soliton amplitudes.

The electron detachment of negative hydrogen ions exposed to a few-cycle linearly polarized laser pulse is investigated in the context of the strong field approximation evaluated by the saddle-point method. The results show that the angular distributions of the laser-induced photoelectron obtained by the saddle-point method are in good agreement with both the experimental results and the numerical-integration results. More importantly, we show that the unusual maximum in the angular distributions of photoelectrons for negative hydrogen ions can be explained by the quantum interference effect based on the saddle-point method.