Symmetries, conservation laws and dust acoustic solitons of two-temperature ion in inhomogeneous plasma

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 [Formula: see text] and [Formula: see text]. 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.