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In this investigation, the effect of polarization force on dust acoustic solitary waves (DASWs) has been presented in a dusty plasma composed of Maxwellian electrons, vortex-like (trapped) ions, and negatively charged mobile dust grains. It has been found that from the Maxwellian ions distribution to a vortex-like one, the dynamics of small but finite amplitude DA solitary waves is governed by a nonlinear equation of modified Korteweg-de Vries (mKdV) type instead of KdV. The combined effect of trapped ions and polarization force strongly influence the characteristics of DASWs. Only rarefactive solitary structures are formed under the influence of ions trapping and polarization force. The implications of our results are useful in real astrophysical situations of space and laboratory dusty plasmas. [ABSTRACT FROM AUTHOR]

An investigation of the characteristics of freak waves in dusty plasma containing two temperatures ions is presented. The reductive perturbation method is used to obtain the Kadomstev-Petviashvili (KP) equation. Further, on modulating KP equation, the nonlinear Schrödinger equation (NLSE) is derived. Under the influence of various parameters (e.g., superthermality of cold and hot ions, a number density ratio of cold ions to dust and a temperature ratio of cold to hot ions), the characteristics of freak wave structures are studied. [ABSTRACT FROM AUTHOR]