In this paper, we investigate dust acoustic solitary waves in dusty inhomogeneous plasma with a weak density gradient. For this, Lie analysis is utilized and solitary waves are obtained with the aid of the newly extended direct algebraic method. The solutions so obtained carry a variety of some new families including dark-bright, dark, dark-singular, and singular solutions of types 1 and 2. The sufficient conditions for the existence of these structures are given. Meantime, the effect of parameters like dust charge, cold ion density, and number density on the soliton structures are investigated in detail, which shows that dust charge affects the amplitude but density does not put any impact on soliton’s profile. A graphical approach is practiced to discuss the physical impact of the problem. Finally, by using a multiplier approach, conserved quantities are reported.

中文翻译：

---

非均匀等离子体中两温离子的对称性、守恒定律和尘埃声孤子

在本文中，我们研究了具有弱密度梯度的尘埃不均匀等离子体中的尘埃声孤立波。为此，利用李分析，并借助新扩展的直接代数方法获得孤立波。如此获得的解决方案带有各种新的家庭，包括暗亮、暗、暗奇异和奇异类型的解决方案1和2. 给出了这些结构存在的充分条件。同时，详细研究了尘埃电荷、冷离子密度和数密度等参数对孤子结构的影响，表明尘埃电荷影响幅值，但密度对孤子的剖面没有任何影响。采用图形方法来讨论问题的物理影响。最后，通过使用乘数方法，报告了守恒量。