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

Theoretical calculations are carried out forstudying soliton’s reflection and transmission in an inhomogeneousplasma comprising ions, two temperatureelectrons and negatively charged dust grains. Usingreductive perturbation technique, relevant modified KdVequations are derived for the incident, reflected and transmittedsolitons. Then a coupled equation is obtained basedon these mKdV equations, which is solved for the reflectedsoliton under the use of solutions of mKdV equationscorresponding to the incident and transmitted solitons.Based on the ratio of amplitudes of reflected and incidentsolitons, reflection coefficient is examined under the effectof dust grain density; the same is done for the transmissioncoefficient which is the ratio of amplitudes of transmittedand incident solitons. The transmission of the solitonsbecomes weaker under the effect of stronger magnetic fieldand higher dust density. However, this leads to the strongerreflection of the soliton.