Propagation of higher-order compressive dust–ion acoustic solitary waves in a dusty plasma with weak relativistic electrons

Higher-order dust–ion acoustic solitary waves are investigated theoretically for a multicomponent relativistic dusty plasma consisting of nonthermal ions, weakly relativistic electrons and mobile dust particles through reductive perturbation technique by deriving modified Korteweg–de Vries (mKdV) equation. Amplitudes of relativistic dust–ion acoustic solitary waves are investigated for different initial streaming speed of ions, weakly relativistic electrons and dust particles and found that there is non-existence region of soliton for some initial streaming of ions as well as electrons. Interestingly, relativistic electron has a region of critical initial streaming speed at which amplitudes of the solitons are equal for different initial streaming of ions whereas for different initial streaming of electrons, the amplitudes of solitons become same after a certain value of initial streaming of ions, which is a salient feature of this investigation. It is also found that the amplitudes of the relativistic dust–ion acoustic solitary waves increase concavely with the increase in dust charges for smaller values of initial streaming of dust particles, whereas the growth of the same is concave for higher initial streaming of dust particles. The width of the relativistic dust–ion acoustic solitary wave is also investigated for different initial streaming of plasma particles.