Evolution of solitons and their reflection and transmission in a plasma having negatively charged dust grains

Theoretical calculations are carried out for studying soliton’s reflection and transmission in an inhomogeneous plasma comprising ions, two temperature electrons and negatively charged dust grains. using reductive perturbation technique, relevant modified kdv equations are derived for the incident, reflected and transmitted solitons. then a coupled equation is obtained based on these mkdv equations, which is solved for the reflected soliton under the use of solutions of mkdv equations corresponding to the incident and transmitted solitons. based on the ratio of amplitudes of reflected and incident solitons, reflection coefficient is examined under the effect of dust grain density; the same is done for the transmission coefficient which is the ratio of amplitudes of transmitted and incident solitons. the transmission of the solitons becomes weaker under the effect of stronger magnetic field and higher dust density. however, this leads to the stronger reflection of the soliton.