Determination of the measure of size (amplitude) of perturbation and its role in the process of enforcing discrete Korteweg-de Vries solitons to modified Korteweg-de Vries solitons as means of continuum hypothesis in a multi-component dusty plasma

Abstract

The role of the order of perturbation required for establishing modified Korteweg-de Vries (mKdV) solitons and determining the corresponding measure of the size (amplitude) of perturbation ϵ in multi-component dusty plasma is investigated for the first time. Various amplitudes of mKdV solitons at critical density σc based on the respective measure of the size of perturbation generated by the corresponding number of dust charges Zd for some values of ion streaming vi0 are presented in Tables in this new pursuit. Many characteristic results of mKdV solitons connecting the totality of the newly established parameters, namely, initial ion streaming vi0, dust charge number Zd, measure of the size of perturbation ϵ, and non-thermal parameter β , are also reported. Further, a new range of non-thermal parameters β occurring in Cairns distribution is also determined in the presence of electrons with quantum effects for this dusty plasma.