Comparative Study of Small Amplitude Dust Ion Acoustic Korteweg-de Vries and Modified Korteweg-de Vries Solitons in a Dusty Plasma with Weak Relativistic Electrons

In the present theoretical investigation of a multiple components dusty plasma consisting of weakly relativistic electrons, mobile dust particles and non-thermal ions, reductive perturbation technique is adopted to derive Korteweg-de Vries (KdV) equation of quadratic nonlinearity as well as modified Korteweg-de Vries (mKdV) equation of cubic nonlinearity. Initial streaming of various plasma species (ions, weakly relativistic electrons, dust particles) in the formation of rarefactive and compressive relativistic DIA-KdV solitons and compressive relativistic DIA-mKdV solitons are found to play crucial role. Amplitudes of compressive relativistic DIA-mKdV solitons are found to be smaller than that of compressive and rarefactive relativistic DIA-KdV solitons for the same set of parameters, which is one of the salient feature of the present investigation. Non-existence region of compressive relativistic DIA-mKdV solitons for some initial streaming speed of ions as well as weakly relativistic electrons are found to exists.