Dark and bright solitons for the two-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch system with time-dependent coefficient

Abstract

In this work, we present Lax pair for two-dimensional complex modified Kortewegde Vries and Maxwell-Bloch (cmKdV-MB) system with the time-dependent coefficient. Dark and bright soliton solutions for the cmKdV-MB system with variable coefficient are received by Darboux transformation. Moreover, the determinant representation of the one-fold and two-fold Darboux transformation for the cmKdV-MB system with time-dependent coefficient is presented.