Abstract
In this paper, we mainly investigate two-fold Darboux transformation and N-fold Darboux transformation in terms of ratio of ordinary determinant for the (2+1)-dimensional nonlocal nonlinear Schrödinger-Maxwell-Bloch equations with reverse-space. It should be mentioned that the questions of one-fold Darboux transformation addressed, results of one-fold Darboux transformation proved, as well as style of analysis borrow heavily, but the determinant representation involved to cope with higher-order Darboux transformation is nontrivial. By utilizing symbolic computation, some explicit solutions including periodic waves solutions, soliton solutions and complexion solutions are obtained for two-fold Darboux transformation. Choosing particular parameters, figures are plotted to show the propagations and interactions of various types of solitons, such as periodic waves, bright soliton, dark soliton, antidark soliton, two-peak bright soliton, two-peak dark soliton and two-peak antidark soliton.
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