Singular solitons interaction of dust ion acoustic waves in the framework of Korteweg de Vries and modified Korteweg-de Vries equations with (r,q) distributed electrons

Two nonlinear evolution equations (NLEEs), namely, Korteweg-de Vries (KdV) and modified Korteweg-de Vries (MKdV) are derived from the dust hydrodynamic model of collisionless, unmagnetized dusty plasma with electrons following double spectral velocity distribution, that is, (r,q) distribution. Regular as well as singular analytic solutions of derived KdV equations and MKdV equations are obtained separately with the aid of the Hirota Bilinear method. Two singular soliton solutions of both KdV and MKdV equations are obtained separately. The efficiency and interactive approach of the heuristic Hirota Bilinear method leads to multiple singular soliton solutions for its beautiful algebraic technique which generates solitons solutions as well as singular solitons explicitly. Then the significance of multi singular soliton interaction has been studied for KdV singular solitons and for MKdV singular solitons in the critical parameter set. (© 2022 Wiley‐VCH GmbH)