Ion temperature gradient mode linear and nonlinear structures in electron-ion plasma, with stationary charged dust grain

Ion temperature gradient mode nonlinear structures are studied with stationary charged dust. The dynamical role here is played by heavy ions. The small amplitude limit influence of various plasma parameters shows that the phase velocity of the mode modifies the overall plasma dynamics. Further, from the solution of the model equations we obtain Kortweg-de-Vries (KdV) and Korteweg-de-Vries Burger (KdVB) like equations, the solution of which gives solitary and shock wave nonlinear structures. Numerical analysis of these nonlinear structures shows that dust number density and polarity have a substantial impact on these structures. The present observation may be beneficial in space and laboratory plasma investigations.