In this theoretical investigation, we have examined the combined effects of nonthermally revamped polarization force on modulational instability MI of dust acoustic waves DAWs and evolution of different kinds of dust acoustic (DA) breathers in a dusty plasma consisting of negatively charged dust as fluid, Maxwellian electrons, and ions obeying Cairns’ nonthermal distribution. The nonthermality of ions has considerably altered the strength of polarization force. By employing the multiple-scale perturbation technique, the nonlinear Schrödinger equation NLSE is derived to study modulational MI instability of dust acoustic waves DAWs. It is noticed that influence of the polarization force makes the wave number domain narrow where MI sets in. The rational solutions of nonlinear Schrödinger equation illustrate the evolution of DA breathers, namely, Akhmediev breather, Kuznetsov–Ma breather, and Peregrine solitons (rogue waves). Further, the formation of super rogue waves due to nonlinear superposition of DA triplets rogue waves is also discussed. It is analyzed that combined effects of variation in the polarization force and nonthermality of ions have a comprehensive influence on the evolution of different kinds of DA breathers. It is remarked that outcome of present theoretical investigation may provide physical insight into understanding the role of nonlinear phenomena for the generation of various types of DA breathers in experiments and different regions of space (e.g., the planetary spoke and cometary tails).

在此理论研究中，我们研究了非热修正极化力对调制不稳定性的综合影响 MI 尘埃声波 DAW尘埃等离子体中不同类型的尘埃声学（DA）呼吸器的演化，该尘埃等离子体由带负电荷的尘埃作为流体，麦克斯韦电子和服从凯恩斯非热分布的离子组成。离子的非热性极大地改变了极化力的强度。通过采用多尺度摄动技术，非线性薛定ding方程NLSE 衍生来研究调制 MI 尘埃声波的不稳定性 DAW。注意到极化力的影响使MI所处的波数域变窄。非线性Schrödinger方程的有理解说明了DA呼吸的演化，即Akhmediev呼吸，Kuznetsov–Ma呼吸和Peregrine孤子（无赖波） ）。此外，还讨论了由于DA三元组流氓波的非线性叠加而导致的超级流氓波的形成。分析表明，极化力变化和离子非热性的综合影响对不同种类DA呼吸器的演变有综合影响。需要指出的是，目前的理论研究成果可能为理解非线性现象在实验和不同空间区域（例如，