Electrostatic wave solutions for a nonlinear coupled system in an inhomogeneous collisional dusty magnetoplasma

• New (3 + 1)-dimensional coupled nonlinear system is established for an inhomogeneous collisional dusty magnetoplasma.
• Classical Lie symmetries of the systems are discussed.
• Exact similarity solutions might describe solitary, shock, periodic waves, and so on.
• Traveling speeds of various waves are arbitrary due to some arbitrary constants and time-dependent functions.

In an inhomogeneous collisional dusty magnetoplasma, a new coupled (3 + 1)-dimensional nonlinear system is derived for the low-frequency electrostatic waves considering the collision between ions and neutrals. It is demonstrated that due to the collision, the scaling symmetry of the system is destroyed. By means of the classical Lie group approach, two types of exact similarity waves are obtained which show three important features. First, various waves can be constructed from these solutions, such as solitary waves, shock waves and periodic waves. Second, these waves may have shears that are time-dependent, linear and nonlinear. Third, the electrostatic potential and the parallel electron velocity possess more freedoms in the sense that they can have either same or different wave forms.