Soliton–cnoidal interactional wave solutions for the reduced Maxwell–Bloch equations**Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11675054 and 11435005), the Outstanding Doctoral Dissertation Cultivation Plan of Action (Grant No. YB2016039), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213). Some

Abstract

In this paper, we study soliton–cnoidal wave solutions for the reduced Maxwell–Bloch equations. The truncated Painlevé analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell–Bloch equations with solitary wave, cnoidal periodic wave, and soliton–cnoidal interactional wave solutions in an explicit form. Particularly, the soliton–cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell–Bloch equations. Finally, we present some figures to show properties of the explicit soliton–cnoidal interactional wave solutions as well as some new dynamical phenomena.